From the Super Mario Wiki
The Brooklyn Bridge is an old suspension bridge linking the New York City boroughs of Manhattan and Brooklyn. It has been mentioned on a few occasions throughout the Mario series, and was even traveled to at one point.
The Brooklyn Bridge is mentioned during several of the show's live-action segments. Additionally, it can be seen during the establishing shot of Mario Brothers Plumbing at the start of nearly every segment.
In "All Steamed Up", Sgt. Slaughter called Mario and Luigi to inform them he was stuck in traffic on the Brooklyn Bridge on his way over to Mario Brothers Plumbing. However, he informed them that since he was driving a Sherman Tank, he could take a shortcut by crashing through the other vehicles.
The Kooplyn Bridge
In the animated episode "Flatbush Koopa", the Brooklyn Bridge was an actual plot point. At first, the Brooklyn Bridge was simply one of the landmarks Luigi pointed out when he and Mario first arrived in Brooklyn. At one point, King Koopa announced that the Brooklyn Bridge, along with everything else to do with Brooklyn, would be dubbed the Kooplyn Bridge once he succeeded with his takeover.
Later on, King Koopa, having ditched Mario and his friends at Coney Island, ventured to the Brooklyn Bridge, along with several Koopa Troopas and Bob-ombs. King Koopa announced that by destroying the Brooklyn Bridge, Mario's group would be unable to catch up with them while he took over the rest of the city.
Mario's group had managed to catch up with King Koopa by this point, but kept their distance from him. Mario and Luigi then left to get help, while King Koopa tossed several Bob-ombs off the bridge, and attempted to blow it up at its base. After doing some minor damage, Mario and Luigi returned with several police officers, but King Koopa used his Koopa Scepter to turn them into bricks, which the Koopa Troopas tossed at Mario and Luigi.
Toad then stole the scepter from King Koopa, and Princess Toadstool used it to turn the police officers back to normal. While the police officers pursued the Koopa Troopas, Toad convinced King Koopa to follow him back to the Mushroom Kingdom, as he was holding his scepter. King Koopa then abandoned his original plans, and left the Brooklyn Bridge to chase Mario's group back to the Mushroom Kingdom.
At the start of "Misadventures in Babysitting", Mario and Luigi accidentally wound up at Junior's house, which led to mild confusion for the two brothers. Mario was easily able to identify where they were, as he could see the Brooklyn Bridge when he peered through the kitchen window.