Sin City mobsters usually tend to hide in plain sight. They pretend to be country clubs, legit casinos, and even the church but they are usually fronts for criminal organizations. Most people know this, though. They just choose to ignore it.
In the Batman comics, The Penguin runs the Iceberg Lounge, a seemingly innocent nightclub, but with areas hidden from the public to deal with things of a more illegal nature. Batman is aware of this and sometimes hangs around the club in disguise to keep tabs on The Penguin's activities.
In The Godfather films, Vito Corleone poses as an "Olive Oil Importer", and occasional references are made to "the Olive Oil business" when characters do not want to refer to what actually goes on. (Subverted in that he actually does have a legitimate business that imports olive oil; it just isn't where most of his money comes from.)
Nino's Pizza in Drive. Doubly so because as Nino's introductory scene points out, he's actually Jewish, and aspires to be held in higher esteem by the Italian Mafia.
In Mississippi Burning, a savvy, Southern-born FBI agent discovers a hangout where some local men are drinking beer. When he orders one, the crooked sheriff's deputy tells him, "You have to be a member to drink here." The FBI agent asks, "A member o' what?" The deputy replies, "The social club," but it's obvious to everyone (including the audience) that he really means the Ku Klux Klan.
The Serial Murders by Kim Newman: Lampshaded — psychic investigator Richard Jeperson is introduced to some very obvious Legitimate Businessmen by the villain, who is auctioning his supernatural powers to be used for assassination. Upon being introduced to them, Jeperson guesses that they're 'olive oil salesmen', in reference to The Godfather example above. They appreciate the joke, but the villain — who is both rather uncultured and a bit of an idiot — is lost.
Impro Fanfic Do Gooders had the "Tokyo Legitimate Businessmen's Club" — probably in tribute to The Simpsons. To their credit, neither the heroes nor the main villain realized their actual purpose until the shoot-out started. Then again, everyone else knows what they really do...
According toThe Discworld Companion, the Ankh-Morpork City Watch first became suspicious that Chalky the Troll was a drugs smuggler for the Breccia when he registered the company name "Hollow Statue Imports".
Intelligence (2006): The protagonist has many front companies, including a shipyard and a lumber business, but his favorite is a strip club called the Chick-A-Dee.
Although they're a motorcycle gang rather than the Italian mob, SAMCRO in Sons of Anarchy uses this trope in the exact same fashion. Everybody knows what they do for a living, but whenever they're accused of being a biker gang by law enforcement officers, they'll assert that they're just a club of Harley enthusiasts. Most of the members are employees of the Teller & Morrow Autobody Shop which is a legitimate business attached to their club house. However, it is clear that it does not get much business (customers tend to be discouraged by too much gunfire) and cannot fund their lifestyle on its own.
In Dharma and Greg, the parents once jointly bought a boat from a friend of Larry's who would soon be needing a lawyer more than a boat. The name of the boat? Innocent Fishing Boat.
Kingdom of Loathing has a Penguin Mafia. They run The Raffle House and Uncle P's Antiques, both which are "legitimate establishments".
In City of Heroes, Mafia Expy "The Family" has a pizza chain. Billboards advertise "Made Fresh. By Made Men." Which is most likely a shout-out or homage to Neal Stephenson's Snow Crash for his Cosa Nostra Pizza, Uncle Enzo and the world's most brutal 30-minutes or less delivery guarantee.
The Sopranos has both the Bada Bing! strip club and Satriale's Pork Store.
The Hairy Ape: Subverted — Yank goes to a meeting of the Industrial Workers of the World, expecting it to be a front for an organization that achieves its goals by blowing things up. The people there assume that he is a government spy trying to entrap their genuinely legitimate organization when he approaches them, and kick him out.
The Outstanding Citizen Warehouse Corporation from The Sims 3, which is your sims' workplace if you choose the criminal career.
In The Godfather: The Game, one suspects that the various families would conceal their businesses better if they didn't post guards around it who smack their fists into the other open palm every time they see you come near. Or outright open fire indiscriminately if your Vendetta with that family is high enough.
There was a small rumor about years ago that SNK's first American offices were actually owned by the mafia as a means to launder their money and had minimal organized management, which is why their infamous localizations were the way they were.
Parodied when Team Rocket is driven away and the legitimate owner comes back...and the whistling noise doesn't stop, because she's old and her dentures don't fit right.
"Don't look behind the poster! There's no hidden switch behind it!"
In Pizza Tycoon, you can order sabotage devices/weapons from stores which claim to sell "joke articles" and "ice cream", respectively. But if you try to buy weapons openly, they'll tell the police, and prison ensues.
In Persona 2, the Zodiac Club is run by the Masquerade, a cult with Zodiac-themed names for its members. In the sequel, the club falls under the ownership of the Taiwanese mob.
The NES game Nightshade has the Pyramid Club, reflecting the Big Bad's fixation on ancient Egypt. There's also an all-girl ninja gang that runs the clothing boutique and a restaurant ("Chopsticks and Ninja Stars").
In The Elder Scrolls III: Morrowind the Camonna Tong, essentially the dunmer mafia, operates one of these in the city of Balmora called the Council Club. The Thieves' Guild also has one in each of the major cities, since they cannot have "real" offices like the legal guilds do, but everyone knows.
The Trope Namer is Fat Tony's hideout. They have a softball team and "family" picnics.
In the episode where Fat Tony's son appeared, the front is "Waste Management".
The Simpsons also has the Ancient Society of No-Homers, which meets at an old Baskin-Robbins with a marquee reading "Abandoned Store".
Also, in "Homer vs. the Eighteenth Amendment", Moe's Tavern becomes a speakeasy when prohibition is declared in Springfield, and changes its name to "Moe's Pet Shop". The true purpose of the place is obvious, but fortunately for Moe, Rex Banner - the guy in charge of enforcing the law - is just as stupid Wiggum. (Maybe even more so; unlike Wiggum, Rex can't be bribed, but he still can't solve crimes worth squat.)
Family Guy: The Mafia do their dealings in the "Pet Store. That's it, pet store." All of the "pets" are cardboard cut outs, and people regularly order "bunnies" in both 12 gauge and semiautomatic (the cops have it bugged).
"Whatever sort of 'bunny' you think would be best for shooting a guy in the head."
Parodied/subverted/etc in one Bugs Bunny cartoon, where Bugs torments a couple of crooks, and finishes up by erecting a huge sign on the side of their hideout. The police find the two crooks in no time.
Played with in The Fairly Oddparents: Fairy mobsters actually do manage waste. Big Daddy's (Wanda's father) company even has the slogan "A Legitimate Business!"
The infamous Kray brothers of London ran several legitimate night clubs which let them mingle with celebrities. Some of the celebrities were prominent politicians who ran interference for the Krays for a number of years, until their criminal activities became so open and notorious that nobody could get away with defending them any more.
For much of his career as a major player in Los Angeles organized crime, Mickey Cohen worked out of a men's clothing shop and referred to himself as a haberdasher.
The Japanese Yakuza gangs stand in an interesting contrast to this trope: they are in no way secret societies, and openly maintain offices. Members may even have business cards. That being said, the Yakuza are known for referring to themselves as "ninkyō dantai", literally "chivalrous organizations."