As a tourist, check out Segway tours of DC. So fun! And of course, the majority of museums in DC are free, so hard to go wrong with so many amazing options. If you're into animals, the DC Zoo is good as well.
A day on the National Mall is great - and it's free! Go online to http://www.visitthecapitol.gov/ and get early morning tickets to the U.S. Capitol. Metro in (Capitol South is convenient) and tour the Capitol then take the underground passageway to the Library of Congress - the largest & most extensive library in the world and one of the most spectacular interiors in the city. Then stop by the Supreme Court (tours if the Court's in session) and walk around the Capitol on the way to the Mall. You have your choice of many of the Smithsonian museums (all free) to visit along the Mall as you walk towards the Washington Monument. Continue past the Washington Monument to the World War II Memorial, Vietnam Veterans Memorial, and Korean War Memorial; ending at the Lincoln Memorial. Don't forget the camera!! A perfect day ;)
If you have a whole day available and a car available, make a trip to Shenandoah Valley or through Virginia Wine Country in the Culpeper and Charlottesville, VA where you find plenty of great local wineries that offer tasting - and often tours. Especially now in the fall it is great to get out there on sunny days.