Gotham City is one of the oldest Eastern urban centers in the US. 

A Norwegian mercenary founded Gotham City in 1635, but the British later took it over. It was also the site for a major battle in the American Revolution.

There is also a story that 17th-century Gotham Village´s first dwelling was, in fact a asylum that predated city´s infamous Arkham Asylum. A man called Hiram was first building a chapel but his partner in crime of murder insisted it to became a sanatorium.

Gotham´s 19th-century patrons envisioned their community as a concrete and steel stronghold for pious righteousness and booming industrial growth, and for many generations the wealth and business ventures of Wayne family bolstered the city´s economy, but it is best known for it´s soaring crime rate, urban legends and Gothic spires.

Location

Gotham City’s actual location was never fully explained. The location would vary depending on the writer. A majority of writers usually put Gotham City on the eastern coast on the shores of Lake Gotham. There have been maps created for Gotham but it has also varied many times. Sometimes Gotham City is based on the actual eastern coast and sometimes it would reside around Manhattan or Vancouver.

Source: http://www.comicvine.com/gotham-city/4020-23611/