Apparently "66% of Twitter users won't give an actual city as their location," so instead they use city nicknames, and according to majority rules, New York City is officially known as "Gotham" in the Twitterverse. There has always been some debate over whether Batman's Gotham City is actually New York City, with Chicago often trying to claim it for their own. Back in 2008 there was talk of New York City officially adopting Gotham City as its nickname, with Hiram Monserrate saying, “I see that as a marketing tool, ‘Come visit the real Gotham City."
Batman writer Bill Finger once talked about changing Batman's locale from Manhattan to a fictional city, pretty much confirming Gotham's roots in NYC, saying: "Originally I was going to call Gotham City 'Civic City'. Then I tried 'Capital City', then 'Coast City'. Then I flipped through the phone book and spotted the name 'Gotham Jewelers' and said, 'That's it', Gotham City. We didn't call it New York because we didn't want anybody in any city to identify with it." [via Laughing Squid]