I don’t leave town too often for camping, however I can recommend a GREAT spot for a day-long fishing trip. I try to hit Fountainhead park (http://www.nvrpa.org/park/fountainhead/) in Fairfax once every couple of weeks for fishing. Renting a john boat plus trolling motor, life vests, etc is only ~$45 for the entire day. The fishing is good, and there are some seriously monstrous bass and catfish in there. Also, the natural scenery is beautiful, and its very common to see beavers, heron, and bald eagles all doing their thing on the water. And the best part, its never crowded.
For out of town, I’ve never camped out, but I’ve enjoyed myself on Lake Anna and on Smith Mountain Lake near Roanoke.