NYC is a walking town, so bring good shoes for hoofing. I'd suggest waking out to the midpoint on the Brooklyn Bridge at least,. You can walk all the way over and take the subway back to Manhattan. The view of the south end of the island from the BB is breath-taking.

The Highline is another great stroll, and it's free. THe south end of the HL will put you in the West Village which is my favorite part of NYC to walk around in. I'd steer clear of Mid-town, Times Square. Nothing there but tourists.

The Church of St John the Divine is also worth a subway ride. It' sup near Columbia University. The largest cathedral in the world, I believe, and still unfinished. It's an awesome place to go and wander around in.

Central Park is also a great stroll.

More later.