Wife and I stayed a week at Lake Fairfax Park (Very close to Vienna). It's a county park with a campground. Sites were nice and level. WiFi, clean bathhouses. Extremely convenient to Activities in Northern VA, DC. If you aren't comfortable driving into downtown DC, you can drive to the Vienna Metro station and then take the subway to downtown dc.
We were the just after Labor Day and the camp store was sadly lacking, however, there are major stores (Grocery, Home Depot, etc,) within about 10 minutes of the park. You're in the heard of Fairfax county but feel very isolated (no traffic noise). There is airplane noise as it can be in the flight pattern for Dullen airport, depending on which way the aircraft are landing.
THey have 30amp svc and water at the sites. They have a conveniently located dump station.
Lake Fairfax Park, Fairfax County Park Authority
Other campers here have written about Cherry Hill in Prince George County on the Maryland side of DC but we've never stayed there. You might search on that name.