The area is full of monuments and museums and such, but to get off the beaten path a bit, try the National Arboretum, Great Falls, Roosevelt Island, Alexandria (Old Town, Del Ray, and Fort Ward Park), Capitol Hill, Manassas (Bull Run to yankees), assorted other battlefields within a days drive, Fredericksburg, the Northern Neck of Virginia, the Eastern Shore of Maryland and Virginia (nice artist's colony in Easton, MD), the Chesapeake, Tangier Island.... I could go on for pages, and then I am sure Flying Camera and others would name spots I have missed. How long are you going to be here and what kinds of things do you want to see?