omg, I used to live down the block from Jazz on the Park. Haha, small world indeed. Around that part of town, there's really nothing super great. A good cheap day is walking down the side of Central Park until you hit the Museum of Natural History. A little bit north is Columbia University and there are a ton of bars and restaurants to try. The Cathedral of St. John the Divine is close, that's an awesome hour to kill. If memory serves, they have peacocks on the grounds that you can feed. When you hit the Museum of Natural History, walk east through the park and you'll hit the Met and that place is awesome. Plus i think they'll still let you in for a quarter. The Whitney and MoMA and museums like that are cool but their tickets are pretty expensive if you're on a budget.
When I lived on that block I was poor as hell and I always walked everywhere, it was pretty easy to get around and nyc is the best place to meander and clear your mind. Good luck and have a great time.