New York is a city that truely never sleeps. Whenever I go, I just walk around for hours and have new sights to see. Impossible to get lost in NYC.
You can pick up a NYC pass (
http://www.citypass.com/new-york) if you think you will be covering most of those activities covered. The observatories provide great views of the city.
Catch a broadway show. TKTS booth (located at Times Square) has got pretty good discounts (33%-50% off) on Broadway and off-Broadway shows running that night. I would recommend getting there earlier as I believe the booth opens at 3.00pm and good seats can go by fast. I have been able to pick up Rock of Ages highly recommended if you are into classic rock) and The Phantom of the Opera.
I love the street food. Restaurants are also great all over town for ethnic and non ethnic foods.
Central Park is a nice visit to see the vast difference between the greenery and the metropolitan jungle.
Museums are great if you are into that kind of stuff. I enjoyed Natural History. Was not too thrilled with MOMA, but Modern Art is not my cup of tea.
Have fun in NYC. Great place to visit.