If you are going to be in downtown DC for the Air and Space Museum I would say the Natural History Museum and the Museum of American History, which are both right on the Mall. The new Museum of the American Indian is really close to Air and Space too. They have a pretty cool garden.
The Spy Museum is closer to Metro center so you'd either have a fairly long walk or have to take Metro. My sister is an elementary school teacher and her comment about the spy museum is that there is a lot of reading so it isn't necessarily great for kids under 10.
If your trip is when Congress is out of session, you can often get really good hotel deals. If not, you might want to look at hotels just off the Beltway but on a metro line. That way when you're ready to head home you don't have to navigate out of the city first. I know there are decent Marriotts in Greenbelt and New Carrollton which have shuttles to Metro. If you are on a serious budget, the Howard Johnsons in Cheverly has low rates and a Metro shuttle. They cater to bus tours.
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Mother to DD-A July 2008
and DD-B-November 2010