A couple of things that I didn't see mentioned:
the Intrepid Air & Space Museum - maybe more to your husband's liking but I certainly enjoyed it - they now have a space shuttle on display -
http://www.intrepidmuseum.org/
Jones Beach air show - which will be the last weekend you are there I think - they have the Blue Angels -
awesome - be sure to take sunscreen, hat or visor, lip protection
http://www.jonesbeachairshow.com/
walk across the Brooklyn Bridge - a traditional tourist thing or so my daughter tells me.
take the Staten Island ferry - free I think
even if you can't get tickets to go to the top of the Statue of Liberty, you can likely get tickets to go to Liberty Island on the ferry and then on over to Ellis Island.
My daughter now lives in NYC and set up our itinerary and we saw almost everything previously mentioned. Take lots of pictures, and a fanny pack comes in very handy.
Enjoy your trip.