Take in a show at a jazz club somewhere in the city. I'd recommend the Blue Note in Greenwich Village (
http://www.bluenote.net/newyork/index.shtml). Reservations are required, I believe. It has been a couple of years since I was there, but it was great!
I'll second Sainters7's suggestion to just walk around Manhattan. Great atmosphere, and you'll come across some less-advertised places to visit and some hole-in-the-wall places that you'll want time to check out. I did that when I went for a girls' trip. Wouldn't you know, we stumbled across the Museum of Sex.
Take the subway to Brooklyn and walk back to Manhattan across the Brooklyn Bridge.
LOTS to do!