According to Carmen Nigro's blog post at the NY Public Library, "English proverbs tell of a village called Gotham or Gottam, meaning “Goat’s Town” in old Anglo-Saxon. Folk tales of the Middle Ages make Gotham out to be the village of simple-minded fools, perhaps because the goat was considered a foolish animal." I guess if the shoe fits.
Gotham City sure had it's cast of characters: The Penguin, Catwoman, Mr Freeze and The Riddler to name a few. None were able to take down the Cape Crusaders or destroy Gotham City. I guess that still holds true, whether you call it Gotham, New York or The Big Apple, it's not going anywhere (despite the NY Daily News Headline from 1977: Ford To New York: Drop Dead).