When you first arrive in Washington, you’ll probably be eager to experience some of the big sites, so it’s a good idea to start downtown. After breakfast, head straight to the Washington Monument and get an assigned ticket for around 12:30. Then, walk down the National Mall to the U.S. Capitol and catch a morning tour there (call your Congressmen beforehand for details and reservations). Try to be out of the Capitol by 11:30 so that you can leisurely eat lunch on the National Mall before you’re due at the Washington Monument.
After climbing the Washington Monument, stay in the area and pick one of the Smithsonian Museums for the afternoon. In the entryway of the popular Museum of American History is Old Glory, the flag that inspired the Star-Spangled Banner. Spend the afternoon exploring this or one of the other Smithsonians, but leave around 5:30 or 6:00 so that you can have an early dinner at one of the nearby restaurants. After dinner, go explore the memorials. Start with either the Jefferson or the Lincoln and work your way around to the other end, hitting the World War Two, Vietnam, FDR, and Korean memorials. If you have a favorite, slow down and focus on it, because you might not have enough time for all of them.
After this very busy day one, day two will be much slower. Sleep in a little and miss rush hour traffic; then take a cab (or your rental car) down the George Washington Memorial Parkway to Mount Vernon. Spend several hours taking a tour of the house, enjoying the grounds and the view of the Potomac. Then, drive back to Alexandria, where you can spend the afternoon and evening shopping, dining, and walking in delightful Old Town Alexandria.