I visit NY at least twice a year, usually for business, and I ALWAYS make sure to add on a few days of leisure time.
It's one of my favorite cities worldwide (with London and Berlin), just being there makes me feel good!
Be there, walk around, breathe in the city, day and night!!
Intrepid seems like a good idea, if weather is fine, go on a boat trip around Manhattan by WaterTaxi (those yellow boats), it's cheap and fun and nice way to get from Intrepid to the Upper East Side (which is a world of its own, and nice, too).
Should you want to see a show, try to get a ticket on the same day, you can buy these at 2 ticket outlets (sorry forgot the name) on Times Square (that would be Broadway and 46th or so) and close to Pier 17, they sell tickets on the day of performance for as much as 50% off.
Oh and btw: You don't want to go to the Bronx...did someone mention that already?