Agree with most of the ideas on here but here are a couple of new ones -
http://www.groundzeromuseumworkshop.com/home.htmlThis is not actually near Ground Zero, but is well worth a visit as it houses the original photos taken by the one official photographer who was allowed into the Ground Zero area in the days and months after the attack. Pre-booking is a must as only a few people (about 20) can visit at one time - but once you are there you can spend as long as you like. Be prepared to be moved by what you see, and if you are lucky the photographer himself will be there.
Combine it with a walk along here - only about 100 yards away from the museum - which gives a completely different viewpoint of the city.
http://www.thehighline.org/ The food and drink for sale up here is pretty expensive though, so maybe buy before you go up!!
Also in the opposite direction from the museum is an Apple store, which may or may not float your boat, but is a great place to grab a bit of air-con before moving on!!
http://www.tenement.org/ is also worth a visit, but again pre-book.
Near Central Park and Bloomingdales take the tramway across to Roosevelt Island (we did this on our last morning before going to the airport as it only takes a couple of hours in all).
Again a different view of the city.
http://www.ny.com/transportation/ri_tramway.html It is free if you buy the 7 day subway pass for $30 dollars. We were only there for 4 nights, but it was totally worth the money. If you do, another trip would be to take the tram right down to Brighton Beach and walk all the way along to Coney Island where you can see Nathan's Hot Dogs where the annual hot dog eating competition takes place.
We did all these things a few weeks ago on our second trip to New York, as obviously we didn't want to do the Empire State/ Top of the Rock etc. again, but those will obviously be be top of your list if this is your first visit.
