I stayed at Big Meadows Campground. It is on Skyline Drive. We stayed for a week and it was one of the best trips we have taken. The one downside is no electric or water at the sites, but they do have water areas located all over and you can have generators. Right down the road is a hike to some waterfalls and where the kids and us were able to get wet and stay cool. Deer walked right up to our camper and slept right behind us in the woods. You can go down into a nearby town called Luray and they have a lake where you can swim (there is a charge, but it was not much) and other attractions like a cave you can walk Through.

http://www.nps.gov/shen/planyo.....eID=318211

Hope this helps.

There are a number of campgrounds on Skyline drive itself.  None of them appear to have water or electric, if that matters to you.  Matthew's Arm, Big Meadows and Loft mountain have some reservable sites, the rest are first-come, first-served as is all sites at Lewis Mountain.  Matthews Arm is north of Thornton Gap (US Rt. 211).  Big Meadows is halfway between the two passes (Thornton Gap and Swift Run Gap - US Rt. 33).  If you arrive on a Thursday, you definitely shouldn't have a problem getting a site for the weekend.  Friday can be a tossup during the busy season and holidays.

I've camped at Lewis Mountain, which is a small campground just a little north of Swift Run Gap, and Loft mountain, which is a large campground south of Swift Run Gap.  I've had good experiences at both.  There's lots of hiking opportunities at all of them.  Loft Mountain may be large, but it's spread out over a lot of land, so it doesn't feel crowded. 

If you like doing rock-scramble type hikes, Bear Fence Mountain is a pretty good one with a fantastic view at the top.  I seem to recall it's about 2 miles away from Lewis Mountain campground (somewhere around mile post 58).

http://www.nps.gov/shen/planyo.....rounds.htm