Certainly visit the Aircraft Carrier Museum Intrepid docked on the west side of Manhattan. I don't recall what they have as far as WWII aircraft, but is it a great place to visit. A Concorde and a submarine are on display next to it.
http://www.intrepidmuseum.org/
About 1 hour north of Manhattan is the US Military Academy at West Point. They have a museum.
http://www.usma.edu/museum/
In Rhinebeck, NY, about 105 miles north of NYC, is Old Rhinebeck Aerodrome, which has one of the world's best collection of flying WWI aircraft. They put on a fun barnstorming show in the summer.
http://www.oldrhinebeck.org/
About 115 miles northeast of NYC is the New England Air Museum at Bradley Field in Hartford, Connecticut. Wonderful display and collection of aircraft.
http://www.neam.org/
Washington DC is about 240 miles ( 4 hours by train ) and we have the Smithsonian NASM collections here at the Mall Building and the Udvar-Hazy Center.
http://www.nasm.si.edu/