An hour away from NYC, there lies a summer camp on a pristine lake which was abandoned 15 years ago. I cant tell you where this is, but some research can lead you to the right place.
Webster Hall is a solid venue, and a frequent stop for many great bands on their rise to glory. If you've only got a few nights in the city, chances are a great act will be playing here.
Chuko has the best vegetarian ramen I've ever had. It's kind of ruined me for other types of Ramen. Favorite neighborhood spot with good people running it.