Personally...I would choose a place like Cherry Hill.. While some may think it's a little pricey, it's a safe place to leave your RV. Plus the fact that you will have a cool comfortable place to return to after seeing the sites in DC, since you will have it plugged in and AC on. Given the fact that you will also have cable tv at night (if you like that sort of thing) and a plce to dump your tanks.
I would highly recommend taking public transportation into the city. Even if you park in the city, you will still be doing a heck of a lot of walking. Wear comfortable shoes!