I'd agree with other posters that getting onto the Hudson and NY Harbor is a memorable way to see the city. Staten Island Ferry is the low cost option for sure. A little more classy choice IMO would be these folks:
New York City Sailing, Boat Tours, and Private Charters on Schooner Adirondack, Yacht Manhattan, and Schooner America 2.0 (NYC,
If you are up to it physically, you can rent one of the Citibikes and pedal along the westside on the bikeway.
If your budget permits, I'd recommend an NYC fine dining experience too. Java dog mentioned some classics. You could also check out Daniel, or 11 Madison Park. A slightly less expensive place (not "fine dining") that is unique:
Pure Food and Wine | One Lucky Duck. Their thing is raw food. It's very good, but I suppose not for everyone. They do have a very nice courtyard for al fresco dining.