Concur with Metro to the Mall. There's always street-side parking available within 2-3 blocks of the museum, but you have to know your way around in order to find it. If going to the Mall, the L'Enfant Plaza Station (Blue and Orange Line) is actually most convenient to NASM.
For Dulles, there are a number of ways to get out there.
The NASM bus from Mall to U-H
ISN'T one of them. It no longer exists.
Here are the other options:
1.) Metro to the West Falls Church Station (
ORANGE line) then a Washington Flyer bus to Dulles Airport and then the Airport-Museum shuttle from there.
2.) 5A Metrobus from L'Enfant Plaza (stop is two blocks away from NASM Mall) to Dulles Airport. Shorter, and cheaper alternative to #1, but the buses aren't as nice as the Washington Flyer ones).
3.) Cab from any of the above locations (downtown DC, West Falls Church, Dulles Airport, etc). This is going to be HIGHLY expensive and actually inconvenient. IIRC cabs still have to pay the $15 entrance fee to UH, and there isn't a cabstand there ... so when you're ready to leave you'll need to call another cab.
4.) Personal vehicle (or rental car). IMHO this is the best option for convenience.
At U-H, be sure to ask the docent to tell the story about the live UXO found inside the Do-335 during restoration. They just LOVE to tell that one.
Other aviation/military-related attractions in the area? PLENTY:
Navy Museum at the DC Navy Yard in DC. You need to call ahead and give them your ID info (it's an active military reservation), but its an incredibly neat place and never really crowded.
American History Museum (Smithsonian). Great exhibit on "Americans At War" with some aviation content.
National Museum of the Marine Corps in Quantico. A ways South of DC, but it has good aviation content and is pretty cutting edge in terms of the displays.
If you're willing to venture further South, there are a number of Aviation museums in the Richmond<->Hampton Roads area.
Moving North of DC there's the
Air Mobility Command Museum at Dover DE.
Intrepid in NYC,
MAAM and the helicopter museum in PA, etc.
Lots more stuff as well. More than I can easily go into. I've lived in the DC area for 20+ years now and still haven't done all the attractions, exhibits, museums, battlefields in the area. This area is literally overloaded with stuff to do.