Avra restuarant has the best Greek food in the city; very delicious lamb. Rosa Mexicano has the best Mexican food in the city, as well as the best margaritas. Highly doubtful that you will get a reservation at Peter Luger, best steaks in the U.S., but Ben & Jacks are also great. I don't know the name of the place, but there is this one burger joint in the Village that makes burgers almost as big as your head; if you really want to know the name, I'll look it up.
Museums? Metropolitan Museum of Arts is a must if you haven't been.
Plays? Well, most of them are located around Times Square, but there are some pretty liberal-artsy ones... in the Village. Ever see Macbeth? Okay, how bout Macbeth done by naked actors?
If you want to find out more, just send a PM.
Also, try out this web site: http://www.zagat.com/sem_pages/redirects/static_landing/other_index.html?MID=kw722google&source=google&PID=55
Should give you some good pointers.
