There are a lot of superb museums in the Northeast, some of which I have visited. Some are quite small, but worth visiting anyway. Some of them feature flying aircraft, and some of them welcome fly-in visitors at their own strips or because they are situated at public airports.
I've never met an air museum I didn't like; all of these are either ones I've been to at least once or ones I plan to visit. An asterisk means they have flying aircraft/demos/airshows, a plus sign means they have a public use runway on site or next door. All of them are not too far from some public-use airport, if I'm not mistaken.
All of them have websites, for more info.
If you really like air museums that hold airshows and demos, you MUST check out the annual WWII weekend at the Mid-Atlantic Museum, any weekend show at Old Rhinebeck, or the numerous fly-in and demo weekends at the Golden Age museum.
The incomplete list from memory:
Old Rhinebeck Aerodrome- Rhinebeck, NY *
Golden Age Air Museum- Bethel, PA * +
NJ Aviation Museum and Hall of Fame- Teterboro, NJ *+
Owl's Head Transportation Museum- Owl's Head, ME *+
National Soaring Museum- Elmira, NY
Victory Air Museum- Medford, NJ +
NAS Wildwood Aviation Museum- Wildwood, NJ +
USS Intrepid Air and Space Museum- NYC
Mid-Atlantic Air Museum- Reading, PA *+
American Air Power Museum- Farmingdale, NY *+
New England Air Museum- Windsor Locks, CT +
Cradle of Aviation Museum- Garden City, NY
Western North Carolina Air Museum- Hendersonville, NC *+
There are doubtless many more I haven't mentioned here.
I've also been to the National Naval Aviation Museum down in Pensacola, FL... excellent. Then of course there's the Fantasy of Flight museum in Kissimme, FL... a must-visit on any Florida trip.
http://usnasw.org/