Metropolis is located in Delaware, and Gotham City is located in New Jersey, according to the Atlas of the DC Universe from the 1990s. In popular culture, New York has also earned the term "Metropolis" to represent the city during the day, as opposed to "Gotham," which is frequently used to describe New York City at night. However, "Gotham" does appear in official DC literature. The Batman Encyclopedia notes that "Gotham City was originally based on New York City." Further, it states that although most modern cities are called by the name of their surrounding counties, "Gotham City was unique in that it was actually based on New York City. Thus, Gotham County was really just a friendly nickname that had been adopted by the time Batman first appeared in print." So yes, New Yorkers do call New York "Gotham".