If you do not need hookups, Greenbelt NP is a reasonable option and a lot less costly than Cherry Hill. It is about a half hour walk to the nearest metro station (College Park), or maybe a bit more if you don't walk as quickly as I do. There is a parking garage at that Metro station if you prefer to drive.
Lake Fairfax park in Reston, VA is another public park with camping that is not too far from the Metro. (Their web site has outdated info on that; the Wiehle-Reston East station is the closest within a couple miles as the crow flies, or a bit more if the crow drives.)