Also the Supreme Court and Library of Congress are all right there on Capitol Hill and only takes a few minutes to drop by. (I took my daughter to the Capitol, Supreme Court and White House as the 3 branches of gov't tour.)
You definitely want to fly into Reagan National Airport. Dulles and BWI are quite a distance out. If you don't have a car, be sure your hotel is within walking distance to a Metro stop. In Alexandria, the Embassy Suites is right across the street from the Metro station. While in Alexandria, be sure to spend a little time in Old Town. Great restaurants! Eat lots of good seafood.
If you're into art, the Phillips Gallery is fantastic. I like it more than the National Gallery.
You might want to go to Georgetown as well. A lot of politicians live there, once you get on the side streets, and it also has good restaurants.
The Pentagon has tours. Also, you can prearrange with your Congressional representative to visit their office and a staffer might even give you a personal tour of the Capital.
Even though the Metro is wonderful, bring comfortable walking shoes! May would probably be a better month. Summer starts in June in DC and it can get very hot.
You can get tickets in advance for the Holocaust and Spy museams. Contact them directly before your trip so you can get the days/times reserved before you even arrive.
Metro will get you to most of the major attactions, though you will have to use supplental buses (or walk) if you want to get the places like Georgetown. For $30, you can buy a pass that is good for any Metro (rail) ride you take for an entire week. I believe there is even a less expensive option if you only need it within the downtown zone.
Metro is close to most of the monuments and government buildings, the Smithsonian (except the air and space annex at Dulles airport), the National Zoo, etc. it is definately the best way to travel in the downtown area.