Here are two off the beaten track things you might find interesting
1) free kayaking in the hudson river, whcih is especially cool and beauriful thing to do in the warm weather. you have to know how to swim and wear a life jacket and sign a waiver for 20 minutes on the river. I've done it from 72nd street, but there ar other locationds downtown.
Downtown Boathouse
2) the track and field hall of fame i've never been to it but i know people who are into this and say its a neat place. its in washington heghts off broadway at 168th St, which is off the beaten track for most tourists.
Hall-of-Fame - ArmoryTrack.com