Go out to the west village. There is a restaurant called the Spotted Pig. It's website is
http://www.thespottedpig.com/
Here is the address:
314 W. 11th Street
@ Greenwich Street
New York, NY 10014
I went there about 5 times while I stayed in the area. It's a great little cafe with a bar and a really unique menu. There is also a pretty well rounded wine list. While I was there I saw Helena Christensen with Michael Stipe. I think a lot of celebs hang there. Great spot though.