We stayed in Arlington, found no problems with the Metro, and had tons of options for groceries and restaurants. That was a decade ago.
Not sure how mustachian they are, but also flying into Washington National allows you a Metro stop, great view of DC on takeoff / landing if you pick the right seats, and super close to Arlington. If you want a splurge, also about he cheapest first-class seats you will find, as airlines suck up to Congress.
It's not a museum, but we really enjoyed the Torpedo Factory in Alexandria. There's a bit of a walk from the Metro, but pleasant enough.
If you take the metro to the King Street stop, there's a great trolley that runs in old town all the way down King Street. Trolley stop (which is the beginning of the line) is about a 2 minute walk from the metro station and lets you off 1-2 minutes from the Torpedo Factory. (Stop is on the right with your back to the station and your front toward the waterline. I can't recall exactly what is across from it, but there's an open area with I think brick sloor and a pergola structure.)
Plus the trolley gives you some historical commentary (not amazing insights, but it's a few nice tidbits) and you can hop on and off if there's anything else you want to see. IIRC, the ride takes about 15 minutes from end to end (which would be from the beginning to the stop that I think is closest to Torpedo, which is the last or nearly last stop) and trolleys run every 15 minutes (check for off-season schedule to confirm). And best of all, I believe the trolley is free!
~~Clearly, I love Old Town Alexandria. I used to live there and miss it daily. I'd recommend considering staying there for maybe 1 of their 3 weeks. Depending on which museums, it's pretty easy to get into the district. They could even bike (if they want to rent bikes or their rental has them). I wouldn't recommend it for all three weeks, but I think it would be great for 1.
Also, the Air and Space museum near Dulles*** is fantastic. (There are 2 air and space-themed museums. This one is the Advar Hazy Center, the other is the National Air and Space.) It can be a PITA to get to, but IMO it is so worth it. The Concord and Space Shuttle alone are worth the trip. It can be easy to miss because it's not actually in DC and because people get confused by the other air and space Smithsonian. Like all Smithsonians, it's free, but you do have to pay to park if you drive. (There's a bus that lets off there, too, though.) Without a car, it would be an adventure to get there, but maybe worth it.
