Metro subway is the only way to go. Parking anyplace within a several miles of the National Mall is impossible. You can literally drive around all day looking for a parking spot and never find one.
Most folks who go to DC more than once google the DC Metro map, and pick a station on the edge of the system along their intended route, then ride the rails. from there. Sometimes the second station in has better parking available. Metro goes within a block or so of every place you could possibly want to go.
Whatever you do, do NOT ever attempt to drive a large vehicle/camper/bus into that area. You will NEVER get back out again.