Your best bet is to make a reservation here:
http://www.cherryhillpark.com/They have bus service to the Metro. Should you be going during high season book before going. I'd also suggest staying at least 2 days since there is sooooo much to see and do in Washington but well I'm partial to the city and could easily spend a week just at the Smithsonian, LOL.
You can try this indoor garage. NOT cheap but right in the middle of the city and they have tour bus and RV parking. I'd reserve in advance as the town is filled w/tour buses.
UNION STATION PARKINGGL and have fun.