With only one full day, I would just hang around the Mall and check out the museums (American History, Natural History, Air & Space Museum) and monuments (Lincoln Memorial, Jefferson Memorial). If you want to go into the Washington Monument, you'll need tickets. You can also get tickets for a tour of the Capitol. I'm not sure if they ever reopened the White House for tours since 9/11. If walking isn't your thing (the Mall is huge) you can buy an all-day pass for the Tourmobile at Union Station. It's a tram that stops in front of all the tourist attractions. You can get on and off all day.