Arlington, Virginia is what you are looking for. The hotels are quite a bit less expensive than those downtown, and as long as you select a hotel near a Metro subway station, you can quickly and easily get down to the National Mall and the various Smithsonian Museums. Go into any of the hotel locator websites, such as travelocity.com or hotels.com and look for hotels in the Crystal City, Rosslyn, or Ballston neighborhoods of Arlington. All are safe areas with many amenities, such as restaurants and shopping, and the hotels clustered around the station are within a couple of minutes walk to Metro. Most of the hotels also offer free parking (although you won t need your car, unless you want to drive to someplace further out, such as Mount Vernon).
When I visited DC, I had to drive back and forth from Virginia. Get a rental car for the weekend and give yourself enough miles on the car so you can have fun seeing museums. Go early in the morning for a parking space in one of the lots. Before 6am. Stay in town until after 5:00pm so that you will miss most of the traffic leaving the city. Most of the people working in DC live outside of DC and commute. That s why I drove from Virginia. The further away you stay at a motel from DC, the cheaper the rates. You could get a travel and car rental deal through a travel agent?