For DC, if you can do without the electricity, I strongly recommend Greenbelt National Park. It's just inside the beltway in Greenbelt, MD, and is maybe a half hour to 45 minute walk to the Metro station, and from there the world's your oyster--or at least, the city is. At $16 per night, at least when I was there last year, it's very affordable. Cherry Hill campground is in the same neck of the woods and offers much fancier amenities for a good bit more money; it gets consistently good reviews.
Lake Fairfax Park, in Reston, VA, is also pretty close to the Metro (Wiehle-Reston East), close enough to be reasonable to walk to the station. They have hookups there.
