We live in the Shenandoah Valley so here are a few places we have camped.
1. Jellystone Natural Bridge. Large wooded sites available. Water park, putt putt, swimming lake with beach, etc. Close to... Natural Bridge, Natural Bridge Zoo, Natural Bridge Caverns, Virginia Safari Park, etc. This is myy kids favorite campground.
http://www.campnbr.com/
2. Walnut Hills KOA. Wooded Sites available although the sites are not huge. Pool and Fishing Lake. Nice Quiet Campground not to far from the highway.
http://koa.com/campgrounds/staunton/
3. Shenandoah Valley Campground. Wooded Sites available but are more cramped than I prefer. Overall a nice clean campground with lost of fun activities. My kids love that there are bunnies everywhere you can feed.
http://www.campingisfun.com/
4. Natural Chimneys Campground. Large Wooded Sites available. The sites are more rustic so they are not as level as at other campgrounds. Few Full Hooks. We camp here when we want a quiet relaxing weekend.
https://www.co.augusta.va.us/Index.aspx?page=617
This will be our second season with our camper and we hope to venture out more this year. If you are looking for a Campground with a lot for the kids to do and many attractions close by you can't beat Jellystone Natural Bridge IMHO. Hope this helps.