I would stay in the VA suburbs, fairly close in. The Courthouse area of Arlington has lots of restaurants (Google "restaurants near courthouse metro") and shops within walking distance (Wilson Blvd, Clarendon Blvd.), and the Orange Line metro train has a stop at Courthouse. The Orange Line will get you in/out of downtown pretty easily and quickly.
Look into staying at the Residence Inn by Marriott Arlington Courthouse (closest to metro and restaurants/shops) or Hilton Garden Inn Arlington. Both have limited parking that you pay for on a per day basis (maybe $15/day+tax).
Here's a link to the the metro rail map
Metro - Rail - Maps - Rail/Google Map
Too bad my wife and I are leaving for SoCal then, we'd love to meet you and help you in any way to enjoy your visit to DC. Have a great time!
