I have to say that this thread is pretty helpful as I am going to stay in NYC for a few days next week before I go on to Philly and I need stuff to do.
From my past experience:
Stomp is a very cool show, but it depends on the type of person. I am a drummer so I like that kind of stuff, but some people look at it as a bunch of noise. Whatever show you go to, stop by TKTS in times square the day of the show, where you can buy tickets for cheap. I just want to warn you that there might be a very long line.
The museum of natural history - I was there a few years ago and I remember it was really cool and interesting. Don't know if it will interest a 4 year old, but even for adults it's a lot of fun. Can take at least half a day, if not more.
Madame Tussauds wax museum - They have museums in many places, but if you have never been to one you should definitely go to see it. It is truly amazing.
The USS Intrepid - very cool tour of the retired aircraft carrier. You get to see lots of different planes and helicopters.
If you are technology lovers, you must stop by B&H. It is a Photography/audio/video heaven. The store ceiling roller system is awesome and they have great prices.
ESPN zone - very fun place to spend a few hours in. Just watch out not to keep on putting more and more money on your card.
NBC studio tour - the NBC studios are located at Rockefeller center. The tour was really cool and interesting. Takes about an hour and a half.
Also being an audience on a TV show is fun. I think you can do this online on the show's site.
If you get a chance, stop by the Marriott Marquis hotel in times square. Take the elevator up to the 49th floor and you will be amazed...believe me, it's very cool.
