There is a Gotham city in England. I've been there; it's very small. At the local bus station there is a clock with a Batman bat in it, to tell you the bat time in Gotham. There's a nice old church there, but not much else.
In the middle ages, a series of stories about the "wise fools of Gotham" were circulated. To avoid a tax from King John, the people of Gotham acted crazy and avoided a royal visit (and tax). "Wise fools" is often changed to "wise men" of Gotham. The name was popular for about four hundred years before it was applied to New York City. I have seen a woodcut of "Gotham" dating around the American revolution. The name was applied to other American cities, such as Philadelphia.
Washington Irving is notorious for borrowing the stories and legends of others. "Gotham," meaning New York City, appears in Salmagundi; or, The whim-whams and opinions of Launcelot Longstaff, esq. (1807). The book was written by both Washington Irving and James Kirke Paulding. For some reason, the latter author is not credited today. Although Paulding is not known today, he was famous in this period; lack of posthumous fame is no reason to discredit him.
I'll post other American "Gothams" of this period as I find them in newly digitized databases such as Early American Newspapers.