Liberty island (and Ellis island) is still closed due to
Hurricane Sandy damage, set to reopen july 4th
I enjoyed the museum of natural history. It includes the hall of meteorites which has a nice 34 ton piece of iron as its centerpiece.
Make sure you have a meal in a deli. Some of the sandwiches you get there are fantastic. If you want a challenge try
Carnagie Deli
A more sombre place to visit would be the 911 memorial