So I wouldn't even necessarily call this place a campground, more like a spot to camp. Spy Rock is this awesome hike about an hour away from Charlottesville, Va. It is a great hike with a small rock scramble at the top for an extra bit of fun. Not only that, but the top has almost 360 degree views of the Shenandoah Valley.
Basically, at the top before you do the rock scramble, there is a little clearing meant for camping. Sure you have to cart all of your crap to the top with you, but TOTALLY worth it once you catch that sunrise from the top of the mountain. Plus the clearing is an awesome spot to camp. Flat, open, space for a fire. What more could you ask for?
This is one of my favorite hikes in the Shenandoah Valley.
Also, as long as you're close, might as well hit up Charlottesville. I went to college at the university of virginia, so I know the area well. There is no better city than cville. Amazing food, concerts, great hiking, sports, history, and beautiful scenery. If you're looking for something to do in the area, go visit Monticello (TJ's house), go to a winery, see UVA's campus and take a historical tour. There are so many options. Not to mention the Sky Line Drive which is only a short drive away.
Do this hike, stay on the mountain, and go visit cville. I promise you won't regret it.