The permanent piece called "Meeting" at MoMA PS1 is an etherial experience of light and color and quiet. Sit and look through the cutout in the ceiling and watch the light change both outside and in. You can't tell what you're looking at until maybe a bird flies by.
Dead Horse Bay is about an hour and a half from lower Manhattan by public transit, but well worth the journey. There is so much glass on the beach that the waves make a soft tinkling sound as they roll in. It’s a scavenger’s dream, and glass isn’t the only thing you’ll find here. There are still plenty of horse bones to remind you where the place gets its name.
Coney Island is the best for everything - the beach, the rides, the beer - but mostly for the Skee Ball. It's incredibly addicting, affordable and satisfying (depending on your aim).