Hi E.,
Just FYI, the Smithsonian is not A museum, its ALL the museums in a collection around the capital mall (I think Night at the Museum, confused a lot of people :) )
They're all FREE though, so no need to feel like you have to do/see everything... if you get board you just leave.
For 11 and 8 (and you) I'd recommend the Air and Space and Natural History for sure. They're close to each other and you could easily get to both in the same day. Beyond that, do the museums with topics that interest your family.
Take a walk on the Mall, and around the Tidal Basin too. That's a nice way to check out several of the monuments.
Go to the Old Post Office Building. The building itself is cool, but even better, you can go up in the tower and get a great view of the WHOLE city! Many like it better than the view from the top of the National Monument... which may still be closed when you come, anyway.
The zoo is nice... but it isn't really better than any other major city zoo, so if you only have two days, I'd skip it in favor of things that are more DC specific.
Stay anywhere in DC near a metro line. You can stay in Northern Virginia or into Maryland, but even if you're right on the metro line, you're giving yourself time on the Metro that you didn't need to. I'd try to stay around Metro Center or Gallery Place. You can get on metro quickly (pretty much all the lines) but can also easily walk most places you'd want to go.
HTH