There are two "Air and Space Museums". The one downtown on the mall with all the other Smithsonian museums and the new one out by Dulles airport about 30 miles West. They are both worth seeing.
I still live in the Northern VA area and most recommendations for places to stay are spot on. I like the Embassy Suites in Alexandria recommendation and would add the Key Bridge Marriott in Roslynn to the list.
Make sure any hotel you chose is very close to the metro. Arrange for a car service, taxi or rental car for a day to go to the Dulles Air and Space Museum.
Also this area has a plethora of great restaurants with every type of ethnic food. So enjoy some of those while here as well. This is not a low cost area to dine out so be prepared to spend. A good dinner in this area will be $50 a person plus any drinks.
Try this link for good dining in the area
The 100 Very Best Restaurants 2013 | Food & Drink | Washingtonian