I live in DC, in West End, one of the neighborhoods mentioned by another poster, and it's in a pretty good location and is filled with hotels (between Dupont Circle and Foggy Bottom). Within 3 blocks of where I live there is a Wyndham, Summerfield Suites, Embassy Suites, Hyatt, Fairmont, Ritz-Carlton, Marriott, Westin, and some smaller, local hotels (like Washington Circle). I would recommend this area because you are between 3 metro lines: the Blue and Orange lines at Foggy Bottom, which take you to the monument stops downtown, and the Red line, which also goes downtown, but to different areas. It's also convenient because you you fly or take the train in, both National Airport and Union Station are on these metro lines. Also, Dulles Airport has a shuttle that takes you to the Orange line and from BWI Airport you can take a train to Union Station. This may not seem that important, but DC cab fares can really skyrocket for tourists as they don't use meters, you're charged by zones. So essentially, if you don't tell the cab driver exactly which roads to take, he will take the ones that cross the most zones so your fare increases. So if you can walk or get a cab from a metro near your hotel, you'll save lots compared to taking one directly from the airport.
Outside of the Foggy Bottom/West End/Dupont area, I agree that the JW Marriott and Embassy Suites in Chevy Chase/Friendship Heights are very nice and both right on the Red line. We had friends visit us in December who stayed at the JW Marriott and loved it, and I work at a day care in the Chevy Chase Plaza so I can tell you that the Embassy Suites there is in a great location too-very close to many restaurants and stores-though it is further away from downtown. Crystal City is another good location, very close to the airport, but like mcnuss said, it is filled with hotels and apartment/condo buildings which can take away from the DC feel, but there is the DC skyline view and you're very close to the Pentagon and Arlington Cemetary. Even though it would save you some money to stay outside the city, I think you'd really get that DC experience better staying in the city, plus the proximity can't be beat (I can walk to the Kennedy Center and Lincoln Memorial from my building). That way if you don't want to take the metro, you don't have to since you're close enough to walk. Wherever you decide to stay, have a great trip!