Its New York City! Just walk and discover. 24 hrs! Battery Park City is deserted at night. Beautiful Statue views. Long Riverside walks. Enjoy!!
One world trade center is nearby. There are lot of bars and pubs. You may want to check out Irish American Pub. They have really nice beers.
Try walk the full length. The skyline is amazing at all times, but particularly at night
Cecconis is a nice restaurant right by the water (stunning view). There's also a few more a block away. As for activities I'd say take a ferry since rock climbing and the carousel are usually closed at night.
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