Are you in the city or out in Garden City Long Island like your callsign data says?
There's a huge difference.
But in both places, putting up a small antenna can be done without a permit. It's unlikely anyone will bother you. When I lived in Queens, I've put up J-Poles and HF verticals without issue.
Putting up a tower is a different matter. You would have to go through the building dept.
The building dept has a website at http://www.nyc.gov/html/dob/
You can alternatively call 311 and speak to a human. 311 is your one stop shop for information in the city.
You may want to talk to Frank Fallon, N2FF, who is the division director for the hudson division. He's had some experience with New York antenna restriction cases.
You could also talk to Mike Lisenco, N2YBB, who is the NYC/LI SEC. He lives in Queens and is a friend of mine, so if you talk to him, tell him Ryan AB2MH said Hi.