Walk the High Line. It's an urban hiking trail above the city on an old rail line. Go early or it will seem like Grand Central Station. I hope your weather is wonderful. You'll end up near NYU, not far from Washington Square. Walk there and hang out. Bring a picnic.
I did the walk on August 16 and it was so interesting. Lots of sudden sculpture. The high part of it is about 1.5 miles and takes about half an hour, but you can also stop at the high pub. If you go north to south, you can cross over to Riverside Park and continuing walking south to the ferry terminals that take you over to Liberty Island and Ellis Island. I highly recommend the Museum of Immigration on Ellis Island.
Chagrined to discover I've never heard of this before. How long is the walk, lil? It looks ideal. I might have to put this first on my list of things to do, actually.