Dulles is the major airport in DC and that would probably be your best bet. There's a Metro stop right at the airport. There's also a Days Inn just down the street a little from the Metro stop where the free shuttle picks people up to take them to the tournament site, so if you need a hotel that's one to consider. There are also a few hostels in D.C. but I have no idea where they are in relation to the tournament/Metro stops.
Jess, if you're going we totally need to meet up