Much better than the popular Atlantic Grill (near Lincoln Center), we think: Blue Water Grill on Union Square, very good jazz too, and no horns. It's a pleasant walk from Classic Stage which we frequent. We saw the fine Hamlet there recently.
There is more theater in NYC than in London, and lots of it (Off- and Off-off Broadway) is affordable and excellent. Lots of actors in NY.
Union Square - just one of the hundred fun neighborhoods of Manhattan. Just slightly north of Greenwich Village.