I’m a museum fan, so I would find a bunch of odd little museums here and there, but you can do a whole day in the Metropolitan and/or the American Museum of Natural History if that’s more your thing. I would take in a play at a small theater or two, I would wander into Chinatown for lunch, I’d hang out in the Public Library for a bit. The site Hopstop.com gives lots of good info for getting around, whether by foot, cab, or public transit. Go to Grand Central Terminal and gawp at the ceiling. Have fun!