I wouldn't dream of taking a towable RV into DC. Parking is at a premium and often very difficult even with a small car. We stay at campgrounds in the surrounding area for a few nights and take the train/subway into DC to do the museums, etc. Most recently, we stayed at Joint Base Andrews (formerly Andrews AFB) and did "the DC thing." There are a couple of Walmart Supercenters in the area, though. You could check with them and see if they allow RV parking. You could then get an Uber or take the bus to the nearest train/subway station.
Rob