2. A short, scenic drive down the road from Old Town is Mount Vernon, which every American should visit.
3. Take a boat ride on the Potomac from Alexandria down to Mount Vernon or upriver past the great monuments.
4. Do Not Miss Arlington. (My father will be buried there the first weekend in May.) Arlington is very beautiful and moving. It's crowned on Arlington Heights by Robert E. Lee's house which is worth a visit.
5. Annapolis, Maryland, another short drive.
6. The battlefields of the Civil War--all of Northern Virginia is one big battlefield but there are strip malls on most of it except Manassas. If you can spare a day for it, every American should visit Gettysburg, which is 2 (scenic) hours away.
7. A self-tour starting on upper Connecticut Avenue at the Washington Cathedral, proceeding to the gardens of Dumbarton Oaks, in Kalorama, and then down to the shops and lovely houses of Georgetown.
8. The Library of Congress--gorgeous!
Gettysburg is sorta ruined for me by all the statues every few feet. Antietam (even closer than Gettysburg) looks 10 times better with 1/10th the crowds.