Popular destinations, and for good reason: Washington Monument; the Mall and Reflecting Pool; Jefferson Memorial; Lincoln Memorial; The White House (a drive past is sufficient); The Capitol; The Smithsonian (all of it); National Art Gallery (technically part of the Smithsonian); Air and Space Museum (ditto); The Wall (Vietnam Memorial); Arlington National Cemetery (and the Tombs of the Unknowns); Ford's Theater; FBI Headquarters; National Archives (Constitution and Declaration of Independence); Library of Congress; Supreme Court... too many great destinations to see in a short trip - don't miss the minerals and gemstones collection in the Smithsonian Museum of Natural History, and The Museum of American History is a must-see, too!
It isn't the right time of year for it of course- but my favorite vantage point for the DC Fourth of July fireworks is on the steps of the Lincoln Memorial. It's a HUGE mob scene, but the view and the photographic opportunities are absolutely *stunning*.
The Reflecting Pool is in the foreground, and the lighted Washington Monument and Capitol Dome are in the background.
Mind-blowing, the first time I saw it.