I am not just asking for the best shoots but also where to take the pictures from.
I recommend taking a trip over to Brooklyn via the Brooklyn bridge and going down to the river side. Some classic shots of both the Brooklyn and Manhattan bridge can be got, particularly at sunrise / sunset.
I really enjoyed the city view from the NBC building's observation deck.
Soho, chinatown. Check picaspot.com for more ideas
It's probably rather cliché, but you really can get some amazing photographs just walking around Times Square at night. Also, when I was there a few weeks ago, I noticed that if you go late enough (after 1:30 AM, say), there will still be people present, but the crowd will have thinned quite a bit. Whether this is useful or not depends on just what sort of photos you want, of course.
I think the streets of Soho and Chinatown offer some of the best spots to take pictures in New York. I also agree with the Brooklyn Bridge recommendation. Check picaspot.com for more suggestions