Given more time I would have done much more, but from my two day 'memorial' tour, I strongly recommend the following:
Arlington National Cemetary: The history and the sacrifice is readily apparent and inspiring. Visit the Tomb of the Unknowns, John F. Kennedy's gravesite, the Robert E. Lee House, and the graves of great war heroes such as Audey Murphy.
The Korea and Vietnam War Memorial: They are located within a few hundred yards of each other in the 'Mall' near the Lincoln Memorial.
The Holocaust Museum: This is one of the finest museums I have experienced. Very informative and very effective in portraying the horror of the Holocaust.
The Mall: This area in the center of Washington D.C. is where you will find most of the monuments. The Washington Monument, the Capitol Building, the Lincoln Monument and many others are located around the mall. Everyone will recognize the 'Mall' as the location of many historic rallies. The White House and more museums than you could see in a month are located around the mall.
Spend a day in Old Town Alexandria. It's a fun, relaxing day.
Quick Tips:
All the museums are free. See as many of them as you can given the time you have, but pick a few and see them thoroughly rather than rush through more than you can handle.
If you like to run, run around downtown and the 'Mall'. You will cover alot of ground and it will help orient you for sightseeing later in the day. This was one of the best runs I have ever had on vacation. Another great run was along the water in Arlington, Virginia (near the Pentagon and Arlington Cemetary) across the river from D.C. The view is fantastic and the route is very enjoyable.
If you have a relative buried in Arlington, get a pass at the Welcome Center. With a pass, you can drive in and around the cemetary in your own car.
Bring some comfortable shoes...you will do alot of walking.
Drink lots of water...it's hot in the summer!
Best Way To Get Around:
I prefer having a car to get around Washington D.C. It is the best way to see the different sections such as Alexandria, Georgetown, Embassy Row, Arlington and downtown.
When seeing the 'Mall', walk. It is a long walk, but very scenic. Parking in this area is a nightmare, so once you find a good spot, don't lose it.
Several tours are available. I don't usually like tours, but one that is fun is the Duck Tour. You ride in an amphibious vehicle that drives through D.C. and then goes into the Potomac river for a river cruise. With so many sights, a guide adds alot of nice perspective and history.