Prince William Forest Park (south on 95 maybe 20 miles) has both primitive and car camping sites. I've camped there, pretty nice. That is probably the closest - check out this link: http://www.nps.gov/prwi/pphtml/camping.html
Sky Meadows State Park, out 66w (maybe 40 miles) almost to Winchester has a dozen primitive camp sites. I've never camped there. Here's their website:http://www.dcr.state.va.us/parks/skymeado.htm#Overnight
You can also camp on the beach in MD at Assateague Island, but that is a good 3 hours drive.http://www.nps.gov/asis/camping.htm
Car camping is allowed at Burke Lake Park in Fairfax - I've heard this is a great for family camping as well as Bull Run Park in Prince William. Car camping also allowed in MD at Gambrill and Cunningham Falls State Parks (North of Frederick, about 90 minute drive) - watch out for "W" and his Secret Service domestiques mountain biking on the Gambrill Blue Trail.