A note on the Udvar-Hazy center: admission is "free" but parking is $12. I think there is actually a shuttle bus nowadays that goes there from IAD.
Other must sees:
- I agree on the Holocaust Memorial Museum. Perhaps the most well-done museum I have seen anywhere. To go through the main exhibition you will need to reserve tickets ahead of time; this can be done online.
- Vietnam Veterans Memorial ("The Wall"). Not only a revolution in memorial design but an important glimpse into the societal impact of the war.
- National Museum of Natural History. There is a magnificent new mammal hall.
- National Archives. View the Declaration of Independence, the Constitution, and the Magna Carta.
- Ford's Theater. For a play or for the history.
I would recommend that you take the time to walk along the Mall as well.
Re the Indian museum, I have found it somewhat disappointing. The cafeteria is great, though.