JoJo's Bizarre Adventure: Phantom Blood gives us Ogre Street, a fictional section of London. The first thing Jonathan Joestar sees when he enters is a stray cat eating a puppy. Right after that, he's beset by some thugs. Upon hearing that Jonathan entered the street, Dio Brando (Who bought poison from a shop there) decides that he won't need a murder plot of his own, as the locals would do it for him. Unfortunately, Jonathan is far tougher than the first group that comes after him, and his chivalry is enough to impress Speedwagon, who dedicates himself to helping Jonathan.
The fictional Thai city of Roanapur from Black Lagoon is regarded as the criminal capital of the world.
The Zaraki region of Soul Society in Bleach. When the Blood Knight comes from there and treats slicing up people and smelling like blood as everyday activities, that's because there's a really bad place. Makes one wonder how Hell would be...
Since the World Government only controls one Island there, the second half of the Grand Line, dubbed the "New World" controlled by the Four Pirate Emperors, is rather chaotic.
Mock Town on Jaya is a partial example. While pirates have the run of the town and often fight and kill each other, they tend to leave the townsfolk alone, if only so there are people to buy food and booze from. Also, the fact that pirates spend money like water means that the economy is booming.
Saobondy Archipelago, while has lovely shopping areas and a thriving theme park, has a "Lawless area" where crooks and slavers operate uninhibited. After the Time Skip, during which the Navy moved their headquarters to the other side of the Red Line, the size of the lawless area increased.
Fishman Island has the Fishman District an area underneath Fishman Island proper (The "Island" is encased in a gigantic bubble), where the New Fishman Pirates have set up base. It was supposed to be a home for orphans, but quickly fell into disarray. King Neptune has the entire district closed down when it becomes apparent that the negative enviroment was what contributed to the New Fishman Pirates' warped mindsets
Subverted in Princess Mononoke. When seen for the first time, the Ironworks are a bunch of grey roofs and tall smoking chimneys crowded together on a small hill surrounded by heavily barbed barricades inside the rotting stumps of a razed forest. But once Ashitaka gets inside, the steel workers are astonishingly well mannered and cheerful people who hold their equally charming director in very high regard.
Lux in Texhnolyzeis this trope. The parts of the city that aren't in the control of three vicious gangs struggling with each other are in hopeless squalor, and the "normal" populace can easily be more dangerous than the gangsters in those parts.
Crashtown in Yu-Gi-Oh! 5D's. This was originally founded as a mining town to mine a precious mineral called dyne which is used to build D-Wheels, but was eventually taken over by two criminal gangs, who fought each other over the mining rights, eventually using dueling to conscript members into slave labor. The whole arc shows that there is No Honor Among Thieves when Yusei is used as an Unwitting Pawn for one of the leaders to win the conflict, only for him to be double-crossed by his brother. (At the end, the whole roster of Team Satisfaction comes together to bring the criminal rule to an end, making the conclusion both symbolic and satisfying.
The city that Alka visits in episode 2 of Blade & Soul, and the one Karen runs a restaurant at. At one point, a guy dies on the street, only for a nearby guard and then several other people to start searching for valuables on his body.
The Underground from Attack on Titan is an abandoned settlement built in caverns beneath the Capitol, and a place where the most destitute struggle to survive. Overrun with criminals and those with nowhere else to go, it is a place even the military avoids whenever possible. Levi grew up there, and describes it as a trash heap he and his friends were desperate to escape.
Lost Angels in Heavy Object is almost completely overrun by four criminal gangs which are actually fronts for spies from the four superpowers, and they're not shy about using military hardware against one another. The remainder of the population consists of actual criminals profiting off the "gang" wars or people effectively exiled from the rest of society.
In Tokyo Shinobi Squad, Tokyo has become this following Japan's attempts at super-globalization. It's riddled with massacres, terrorists attacks, organized crime, and corruption. It has the highest crime rate in the world and people freely hire shinobi as assassins, bodyguards, and spies.