Trails/Camping in Mid-Atlantic region?

[zip04]

I am currently stationed in Virginia Beach, VA and am looking at taking my wife, kids, and dogs on a 3 or 4 day camping trip. I prefer remote primitive camping where we are alone (I do not want to have to have my dogs on a leash, etc.). Ideally, we would like to be either in the mountains, on a creek, or both. We love to hike, so good trails would be a huge plus. Are there any good spots off the beaten path in either Eastern West Virginia, anywhere in Virginia, or anywhere else within a 6 hour drive?

Thanks for any assistance.