The numerous addresses shown within the film place Gotham City withing the state of New York, and all phone-number area codes and ZIP codes correspond to New York City. New York City was one of the original inspirations for Gotham City.
In the scene with Barbara Gordon's roommate in college, the background music is "Am I Blue", which has another connection to Batman. It also is featured in the animated Justice League: This Little Piggy (2004), in which Batman sings this song on stage in order to save a friend. Batman & Mr. Freeze: SubZero (1998) and Justice League are part of the same larger universe and continuity.