Spend the morning at Arlington National Cemetery. While you're there, don't miss the changing of the guard at the Tomb of the Unknowns, every hour or half hour, depending on the time of year. A short detour north of the cemetery brings you to the Marine Corps War Memorial, a giant bronze rendering of American soldiers planting the flag on Iwo Jima during World War II—one of the most famous images in U.S. military history.
After your contemplative morning, head back across the Potomac to spend the afternoon in Adams Morgan and Dupont Circle. Lunch at one of Adams Morgan's Ethiopian, El Salvadoran, or Mexican restaurants, and browse the Dupont Circle art scene—there are offbeat galleries tucked into the side streets, as well as the renowned Phillips Collection.