The Air and Space Museum out at Dulles airport is much better than the one downtown, but it's a haul to get there from downtown.
I can't believe nobody said the Jefferson Memorial. It's one of the best. From there, go to the FDR memorial, which is often overlooked but excellent. If you want to get away from monuments for a bit, go to Georgetown and poke around. And don't just go on M and Wisconsin streets, you'll miss a lot.
Old Town Alexandria is another place that is similar to Georgetown and is a lot of fun.
Go to the National Gallery.
Check out the Marine Corp Memorial (Iwo Jima) across the river in Rosslyn. Also go to the Air Force Memorial near the Pentagon. And you definitely need to spend time at Arlington Cemetery.
Chinatown and U street are two fun neighborhoods to look around in.