I live there but gay clubs I can't help you with since I don't go clubbing, I'm a more cafe relaxing type of guy.
In Manhattan you shouldn't be worried about too many places, just walk around, enjoy. If you visit Queens, I would suggest trying Astoria(my neighborhood), lots of cafe's, and just a nice place to relax. Obviously Flushing Park where the tennis center is, Long Island City is very industrial but artsy. Forest Hills is nice, just not much to do there. Anyway, I know Manhattan best, you'll be fine pretty much wherever you wanna go. If you don't wanna go to Harlem or anything like that for whatever reason, just don't go above 100th street. But I would suggest visiting it, its a great place, culture, architecture.
And yes as I already said in your other thread, you can go to the Tennis Center when the US Open isn't going on.
You should have a great time doing whatever you do.
Manhattan <3 I have been in Canada the last month and I already miss my Manhattan.
In Manhattan you can check out Central Park, the Upper East and West Sides, Midtown, which has lots of stores, Empire State Building, Rockefeller Center(I suggest going to the top in the observatory.) Then you have Chelsea and the West Village(SO NICE), Also Union Square, Soho, Tribeca, Downtown. Lots of places.
When are you visiting btw?