Academy City in A Certain Magical Index. The city is famous for grooming powerful power users, but it also has a dark side. The "questionable" research that's done at the city leads to many story arcs in the anime, and is enough to for a complete spin off: A Certain Scientific Railgun. They're under international law, which apparently explains why this is considered "legal" there. The city is also far ahead of the outside world in terms of technology, and they have to use this to their advantage in order to make sure more unruly Espers (and powerful) don't go on a rampage. This may also fall under Academy of Adventure as Academy City is made up of dozens of different schools.
The importance of Karakura Town, a fictional district of Tokyo, to various spiritual entities in the anime Bleach is explained by an area of "high spiritual density" (a phenomenon which occurs more or less randomly across the world) coinciding with an area of high population. A notably high population of former Shinigami and other spiritually-attuned beings doesn't hurt, either.
Seireitei in Soul Society might count as well.
Kamakura, a small beachside town some 50 km away from Tokyo, forms the setting for a few series:
Most of the weirdness in Elfen Lied takes place there;
The main characters from Uta Kata spend a lot of time at its beaches, only leaving the town for one Class Trip to Hakone;
The City from Blame! is the epitome of this trope.
Kiki's Delivery Service takes place in a really beautiful port city, which provides an appropriate amount of adventure for pre-teens. It's a case of pleasant dieselpunk.
FLCL takes place in Mabase, a town with a colossal building shaped like a clothing-iron that lets out an enormous amount of steam every now and again. The main character (Naota) is 12-years-old yet has a "girlfriend"/Stalker with a Crush who is in high school, and just about every adult he comes in contact with in the city are presented as childlike and looney. Despite this, he views his life as "boring". If this isn't odd enough, between the beginning and the end of the series, he meets an alien, is targeted by a secret organization, and grows a portal in his own head that creates lumps that eventually turn into giant mecha/plant/anything aliens that destroy most things in their path. Naota himself temporarily turns into a god in the series climax, before letting out a super powerful being that could destroy the planet if it wanted to, but leaves for some reason. Despite everything that happened, he still refers to his life as "absolutely ordinary", said just before a robot with a tv-like head hangs his family laundry.
"Nothing ever happens here, it's all absolutely ordinary."
It's also eventually revealed that the giant iron is a device to be used by the series' villains (the ones responsible for all the killer robots running amok and imprisoning the aforementioned super powerful being) to iron out all human thought on Earth.
Ikebukuro in Durarara!!. Something is always happening whether it's a gang war, Slashers, or vending machines flying through the air.
Fukuoka City in Excel♥Saga, thanks to the machinations of two silly warring entities.
Death City, NV, of Soul Eater is not only the place where the Shibusen (or DWMA, if you're watching the dub) is located, it also holds the significance of being the place where Asura was trapped and, as such, is a commonly targeted place by whoever wants to set him free (which Medusa eventually manages to do, indirectly). And while the students and their weapon partners have to travel around the world for their field assignments, holding the fort is also of utmost importance.
Like most things in Puella Magi Madoka Magica, deconstructed with Mitakihara, the elaborate, beautiful, somewhat-futuristic city full of places where witches roost and are hunted by magical girls. Mitakihara is full of witches because witches are fallen magical girls, and wherever Kyubey goes, there'll be more of both in time.
Morioh in Part 4 of Jojos Bizarre Adventure, which comes with a large concentration of resident stand users (though part of that is because of Keicho creating new stand users with the Stand Arrow.) The heroes' actions even end up adding new landmarks and urban legends to the town.
It is extremely common in solo Super Hero series for the hero to have a specific city that they are known to patrol as "their territory":
Salem Center, Westchester County, just north of NYC (Home of the X-Men's Mansion). They have since relocated to San Francisco, and now reside in Utopia, a rock floating on the ocean just off the US Pacific Coast.
Used straight in Runaways with Los Angeles, with a justification: after the kids take out the Pride, there's a power vacuum and supervillains try to make their niche. But also deconstructed somewhat with regards to New York City, the City of Adventure for the rest of the Marvel Universe - superpowers are seen as something that mostly happens far away from our heroes; then they visit NYC and are awed at seeing superheroes in the streets, and one character comments "here, we're not so special".
Bugtown, in Matt Howarth's various comics, including Those Annoying Post Brothers and Savage Henry. Notable for being infinite in size, and having such screwed-up laws of physics that entropy works in reverse—dead people inevitably come back to life after some time.
Chicago from Savage Dragon. Also, later in the series, there's God City.
Cynosure from Grimjack. Perhaps justified since it was built at the center of the multiverse.
Trantor in several Isaac Asimov stories, which is in fact a city covering the entire surface of a planet. (Timothy Zahn would later adapt this idea to the planet Coruscant in the Star WarsExpanded Universe; it would later appear in the prequels.) A 47th century New York City is used to the same effect in his novel The Caves of Steel. Such a world city is known as an Ecumenopolis.
River Heights and Bayport in the Nancy Drew and The Hardy Boys books. Fridge Logic makes their high crime rates plausible; they were created in the 20's, and were suburbs of Chicago and New York, respectively, so it could be assumed that there's a large influence from the mafia.
One of Leiber's short stories specifically links Lankhmar with its historical inspiration, Alexandria.
Hogboro in several stories by Daniel Pinkwater. In Alan Mendelssohn, Boy from Mars, Alan and Leonard remark on their luck finding that one of the dozen places in the world listed as suitable for interplanar contact is right in Hogboro (though tracking down the exact spot proves troublesome). The next closest spot on the list is in Fort Simpson, Northwest Territories, Canada.
Chicago in The Dresden Files. Justified being due to a confluence of magical leylines in the area and the fact that Chicago is a travel hub in the real world so that draws at least some members of the magical community through there as well. In addition, by later books it's clear that a lot of the action is going on in Chicago because that's where Harry himself happens to live.
In addition, averted in the seventh book when it becomes apparent that there are some really important things going on elsewhere that Harry and the reader don't find out about until later.
Chicago in Wearing the Cape and its sequels: Chicago is the post-Event Metropolis of the Wearing the Cape setting, with good reason; Atlas and the Sentinels created the template for superheroes and superhero teams, and with the Sentinels and the Guardians teams, the city has more superheroes per capita than any other city. Chicago is also the center of the Villain-Rap culture, which means the place is crawling with street-villains and fashion-villains. The Sentinels' reputation is also creating a problem, in that supervillain-terrorists and thrill-villains who want to make their reputations may target them and the city they protect (it has been noted that Chicago was the only freshwater port to get a godzilla attack).
The Sprawl, in William Gibson's Sprawl Trilogy. Officially known as Boston-Atlanta Metropolitan Axis (BAMA), it is essentially one huge megapolis covering most of the east coast of the USA.
Larry Niven did something similar to California.
Thousands of British juvenile adventure novels were published by the pulp presses, and an overwhelming number - somewhere in the hundreds - were set in Calgary. It may be because the writers wanted to show exciting things like cowboys and Indians, ranches, mountain climbers, and hunting (popular subjects of American juvenile literature) but in an Empire setting, and Calgary fit the bill. Many of these books were also translated into German.
The titular city “at the center of time” in Edward Bryant's Cinnabar
True, it's not strictly a city. But the mythical "Bear Country" where the main characters live in the Berenstain Bears series of picture books by Jan and Stan Berenstain almost certainly qualifies, as it is ostensibly an isolated rural community but features many familiar trappings of urban and suburban life (such as a shopping mall) as well as more nostalgic and fanciful settings, like a dank swamp home to roving teenage hooligans and a woman suspected of being a witch. And Bear Country never gets boring for Brother and Sister (although, to be sure, when you're a child and are just seeing many things for the first time, it's awfully hard to get bored).
Deepdene in the Dark Touch novels. The portal to hell in one house doesn't help. Either deamons are coming through it or get drawn to it.
The London depicted in Rivers of London fulfils this role whether it wants to or not.
This is kind of the main idea behind the Quentaris books and the one thing they have in common. (They're not even all by the same author.)
The town of Smallville in Smallville. The explanation for the large number of unusual occurrences is the presence of a significant amount of Kryptonite in the area, which in this case causes humans in its presence to gain powers varying from individual to individual.
Played with in one episode when a Vegas-based rapper claimed it was "the new New York". A certain New York rapper took offense, and a "beef" started.
Forever Knight's Toronto, with a serial killer for every day of the year.
Same with Blood Ties, with monsters taking place of serial killers.
Cabot Cove in Murder, She Wrote. They do get Jessica out and about regularly, but there are still an awful lot of murders in her small hometown — it's a wonder there's anyone left. After Sheriff Tupper left, his replacement in Cabot Cove (an ex-New Yorker) lampshaded this.
Despite all the Adventure Towns the Doctor often visits, aliens in Doctor Who like to invade 20th and 21st century Earth from the Home Counties, usually London.
After two consecutive Doctor Who Christmas Specials bring Alien Invaders to London, the residents turn Genre Savvy and make sure to leave the city at Christmas time.
In Torchwood, Cardiff is located on an inter-dimensional rift, which results in plenty of weird things ending up there.
The town of Sunnydale in Buffy the Vampire Slayer, being set upon a "Hellmouth", is very much a town of this sort. The Hellmouth is described as a portal which leaks mystical energy, both drawing demons towards it and affecting things in supernatural ways: e.g., a girl becomes invisible because she feels invisible, and later we see various kinds of Mad Science that might not work elsewhere. Thus, there is an automatic answer for so many supernatural things all occurring in this one town. The town transformed at need so that in one episode it was small enough to be taken over by a dozen bikers and in others it became a major University town with international sea and air hubs. At the end of Season 3, Xander jokes about this, asking "Why do people still move here?" Turns out people usually stay the hell away from Hellmouths, but the Mayor was actually a hundred-year-old wizard who created Sunnydale as a smorgasbord for demons. After the Scoobies blow him up, the town gradually shrinks, ultimately depopulating completely by the final episode in which it falls into a sinkhole.
Los Angeles from Angel is a more conventional example. Demons obviously like living in the same town as the Occult Law Firm - and Doyle or Cordelia's visions served to explain why Angel usually dealt with them.
In 24, Genre Blind terrorists always make a point of attacking Los Angeles, despite the fact that it is the one city in America that has the indestructible Jack Bauer in it.
In the seventh season, they finally wise up and attack Washington, D.C. But their timing really sucks...
Justified in Power Rangers Lost Galaxy and Power Rangers RPM, as Terra Venture and Corinth are the only cities in at least a hundred-mile radius - Terra Venture is a traveling space colony and there's nothing outside the city but the empty expanse of space; while Corinth is the only city left on earth, the rest of the planet being a bombed-out wasteland.
Also justified in Power Rangers Lightspeed Rescue; the demons limit their attacks to Mariner Bay because the city was built on the site of their old temple and they want it back.
Super Sentai and Kamen Rider work on the same principle, but the events of both series apparently happen in the exact same (unnamed) city every single year. An avid fan will quickly be able to spot reused locations, and come to pity the people who live there.
This city could as well be Tokyo, given the appearances of the Tokyo Dome (which actually sponsors some of the tokusatsu series by Toei) in some of them, among a few other hints.
Except for the one time where it was specifically named Futo which was just Tokyo with a bunch of windmills added everywhere. The TV Asahi building (the channel that airs the shows) was reappropriated as the TV Futo building.
The city of Cascade in The Sentinel. Ebola virus threats? Uranium smuggling? Yakuza gang wars? Paramilitary terrorists taking whole buildings hostage? Just another day in Cascade.
"Seacouver" in Highlander: The Series, especially when Duncan is there. When he's in Paris, guess where trouble happens.
Lampshaded in the In the Heat of the Night TV series, set in the fictional Missisippi town of Sparta. "I should join the Marines...I'd see less dead bodies."
In Big Wolf on Campus, Pleasantville is beset by an astonishing number of bizarre supernatural occurrences; a few of them are connected to the heroes, but mainly it's just a place where weird things happen.
Babylon 5 justifies this trope by having the station be a crossroads for many different space-faring races.
Star Trek: Deep Space Nine: the titular Deep Space Nine space station near the independent planet of Bajor acts as this espeically as the nearby wormhole provides a Plot Magnet to attract others to a space station.
Secret Service is set entirely in Washington D.C., which is apparently just filled with secret agents, Soviet spies, and shootouts between the two.
Mummy has two, one in the USA and one international - Washington, DC and Rio de Janeiro. Apparently, future NWOD games will have a similar setup.
The titular city of Mortasheen is a continent-sized version of this combined with the Industrial type of Mordor, filled with crazy mutants and monsters in a constant state of chaos.
The city of The Edge in the island nation of Al-Amarja is the setting for all the weirdness in Over the Edge.
Ravnica, of the Magic: The Gathering multi-verse, is not quite a straight example, as it's a city that covers its entire world.
It now fits better with the presence of the headquarters of the Infinite Consortium, essentially a multi-planar organization, and several other planeswalkers living there incognito.
Monte Cook's Ptolus, a setting revolving entirely around the titular city (and, incidentally, one of the fattest roleplaying books ever published, at 672 pages).
The city is built around Sealed Evil in a Can and on top of multiple layers of Sealed Evil in a Can, and (mostly unrelatedly) is home to several men who are, or can at least get away with claiming to be, emperor. The evil is leaking, the cans have become something of a tourist industry, and the political tensions are on the rise. Yes, there are some explanations.
Warhammer has Mordheim, a warband setting that takes place in the titular City of Adventure and puts itsownuniqueperspective on it. The city was levelled by a meteorite of Warpstone, a substance that has tremendous value for magical experiments and is a vital ingredient in the Philosopher's Stone- that is, an alchemical concoction that can change "base" metals into pure gold. So, naturally, the city is swarming with violent, opportunistic mercenaries and treasure hunters. Of course, Warpstone is also Toxic Phlebotinum, or perhaps Psycho Serum would be a better descriptor, as it causes physical, mental and spiritual corruption. So, naturally, the city is also teeming with all manner of horrific monsters...
Similar to the Warhammer example above, Warhammer 40,000 has Necromunda, its equivalent of Mordheim. Taking place on the Hive World of the same name, it's justified in that, like all Hive Worlds, the actual planet has been polluted so terribly by eons of industrial production that humans now live in tremendous ant-hive like buildings that serve as the new equivalent of continents.
In the Champions Universe, Millennium City gets far more superhuman action than you would expect for Detroit Redux. Partly justified due to its The City Of The Future meme.
Arkham in Arkham Horror. Home to a number of cults, the infamous Miskatonic University, and far too many eldritch secrets. Most of the expansions add to the madness and make Arkham home to things like a cursed museum exhibit or the only attempted performance of a Brown Note play. A few involve mysteries outside of Arkham and add Adventure Towns to the game.
One sample scale for map-drawing on On Mighty Thews, presumably because of places like Lankhmar.
Sentinels Of The Multiverse: As befitting a superhero setting, the environment decks Megalopolis and Rook City portray expy locations of Metropolis and Gotham City respectively, each with their own hazards and pitfalls for everyone. Megalopolis is a straightforward bright city that at the worst suffers the occasional alien invasion while Rook City is a gloomy locale stagnating under mob rule, corrupt police officers, and plague rats.
The Grand Theft Auto series consistently gives us three of this kind of city since the first game: Liberty City (an expy of New York City), San Andreas (an expy of California and Nevada), and Vice City (an expy of Miami). GTA 2 also gives us "Anywhere, USA", though it's almost forgotten.
Befitting that its borrows a lot from Grand Theft Auto (as listed directly above), Crackdown takes place in 'Pacific City', and seems to be either inspired by, or borrows the idea of a multi-island approach, for geography.
South Town is a focal point for events in the Fatal Fury and Art of Fighting series, and also gets a mention in The King of Fighters series. Appears to be quite a multicultural place, possibily justifying how so many people there master several martial arts from around the world.
The first two Etrian Odyssey games are set in a City of Adventure built around a labyrinth or dungeon; the third features a port town as your base of operations.
In Academagia, Mineta◊ is one of the largest and most important cities in Elumia; as well as the home to "The Academy of Magic of Mineta", more commonly called "Academagia". The game includes many potential events and adventures set in and around Mineta.
Stilwater in Saints Row happens to be a city full of opportunities and if Stilwater didn't had enough opportunities alone, the new bigger city of Steelport is gonna have a lot more than that of Stilwater.
Clint City in Urban Rivals most certainly qualifies. It has gangs, vampires, aliens, robots, pirates...
The city of Hekseville in Gravity Rush. There's always something going on...
Opplopolis starts with a mysterious man assigning Carla Tumblemas the task of going into the city of Opplopolis to uncover the meaning of the word "marvedyne". All of the ensuing action takes place there.
The city of Cwcville in the infamous Sonichu attempts to be follow this trope within the comic's pages, though the author's canonical descriptions of the laws and government in the city outside the comics have made it sound more like a fascist 1984-like Dystopia.
Last Res0rt has its reality show in its very own space station built expressly for this purpose; it houses the show, the arena, and everything else you need for a world-class tourist resort to house and host all the spectators coming to watch.
And in fact, there IS a named city built into the space station, known as the City of... Wonder. Since we're talking about a city manufactured into the space station, it's not that surprising of a name.
The Inexplicable Adventures of Bob! has the "pleasantly innocuous hamlet" of Generictown, which has become a City of Adventure purely because Bob the Weirdness Magnet lives there. Presumably, it would quiet down again if he moved, but he shows no signs of doing so.
Ed: A public school in Moperville, where the local newspaper is sold in neighboring towns with all the regard of a tabloid. We've got a reputation to protect! We can only report on confirmed monsters, like Mega Hogs, or Bigfoot!
Carol: Ed, I grew up in Moperville. Weird stuff happens here...
Later revealed to be a (mostly) Justified example. As it turns out, someone has been increasing the magical energy that exists in Moperville. Because of this, magical beings and whatnot found themselves (and are still finding themselves) being drawn to the town, without realizing it. And by the look of things, it's supposed to get worse soon.
Picture on top: CCC City, the 'City of Opportunities' in the popular flash video series, in which literally every day in and around the city (so large it renders maps pointless) involves countless adventures of many different levels.
The TV series Teen Titans has the Titans Tower in "Jump City", at least according to the comic adaptation Teen Titans Go!; the team's hometown was never named in the cartoon. Meanwhile, "Steel City" is the location of Titans East.
Heatherfield in W.I.T.C.H. (it's where all the portals are, and it's where all the Guardians live.)
The Middle of Nowhere in Courage the Cowardly Dog seems to be some sort of nexus for "creepy stuff", to the point where it takes obvious danger to get anyone but Courage to take notice. Talking animals, aliens, deities, and supernatural entities (not to mention Courage's own sapienceand abilities) are all treated as normal until the big pointy teeth come out.
Springfield in The Simpsons is a deliberate parody of this. At one point Our Favorite Family suddenly notices that they live across the street from an expensive mansion that wasn't there before and was created for that episode so that George Bush could move in.
Capital City is one of these in some early episodes. In "Dancin' Homer", it's even given its own theme song (sung by Tony Bennett, no less) which overtly invokes the trope in its lyrics.
Subverted in which the family travels abroad on occasion, and being them the Simpsons, wherever they go, hijinks follow.
Danny Phantom has Amity Park, a town with ghost/occult-related names for obvious reasons.
Detroit in Transformers Animated, which seems to have had a reasonable population of supervillains even before the Transformers came along. Some of it can be explained by being the centerpoint of the robotic revolution created by Isaac Sumdac.
Lampshaded in one episode where Aladdin is running from a giant floating eyeball and Iago tries to explain to him that he's only dreaming by pointing out how absurd their situation is. Aladdin merely shrugs and says, "Stranger things have happened."
Roll Bots: Flip City provides adventure for all its citizens simply because the roads are all autobahns designed by an extreme sport enthusiast for robots that turn into high-speed spheres.
South Park, Colorado. It can all be summed up in one quote...
Reporter: "And so just weeks after the devastating attack of mutant genetic creatures, zombies and Thanksgiving turkeys, the town of South Park has managed to rebuild itself once again-" (sees giant robotic Barbra Streisand destroying the town) "Oh, Goddamn it, not again!"
Acme Acres in Tiny Toon Adventures felt like this (when the Toonsters weren't traveling around the world and beyond). Having Wackyland next door to Acme Acres certainly helps.
Danville in Phineas and Ferb. Besides the titular characters' physics-defying daily projects, there's a city wide organization of animal secret agents who go undercover as pets, a league of evil scientists and girl scouts who get patches for wrestling alligators.
The poor city of Retroville in Jimmy Neutron goes through a lot of stuff such as a giant plant-teachers, deadly nanobots, giant roaming toys, impending meteors, alien abductions, city-wide hypnosis, the population gets shrunk, pants attack, alien invasions (at least thrice), sentient fast food restaurants, temporary super heroes, super villains, megalomaniac dictators... all caused by Jimmy of course.
in Team Umizoomi, Umi City has its fair share of adventure as well.