This list is far from comprehensive. We would welcome your suggestions.

9/11 Memorial
New York City.

Ellis Island
Access from Battery Park NYC. 212-363-3200

The Intrepid Sea, Air and Space Museum
West Side Highway. Former AirCraft Carrier. 212-245-0072.

Museum of Jewish Heritage
18 First Place, Battery Park City, NYC. 212-509-6130

New York Hall of Science
Flushing Meadows, NY. Overnights, badge work, special theme exhibits. 718-699-0005

New York Stock Exchange
Wall St. The only way to see this is to find a parent who works for a member firm (any investment bank) and have that person arrange to have tickets at the front for the group.  No waiting then. The tour runs 30 min.

The Paley Center for Media (formerly the Museum of Television and Radio)
25 West 52nd St., NYC. 212-621-6800