The Brooklyn Bridge is a bridge across the East River in New York City. Opened in May 1883, it connects Brooklyn and Manhattan with each other.

Donatello fighting against Bebop on the Brooklyn Bridge
One of the levels in the Manhattan Project video game is set there. The level boss is Bebop.
In the IDW continuity "Invasion of the Triceratons" story arc, the Brooklyn Bridge is the only bridge connecting the island of Manhattan with the outside world that is reported not destroyed amidst the urban warfare, but it is otherwise not specifically shown in-story.
The Turtles meet with Superfly and the other mutants beneath the Brooklyn Bridge during the film Teenage Mutant Ninja Turtles: Mutant Mayhem. During the doubly-mutated Superfly's rampage, he destroys the bridge.
The episode Bishop Makes Her Move of the Tales of the TMNT series shows the Brooklyn Bridge being repaired.