I've been taking my kids camping for 10 years (they're growing out of it, but not me), and this is one of two campgrounds I keep returning to, the other being Douthat State Park.
Montebello is in a valley in the Blue Ridge Mountains, and as such, is generally cooler than the localities around it. The road from I-81 is twisty, which doesn't bother me, but if I had an RV, I'd probably come from the Lynchburg side.
It's quiet, the tent sites are nice and the bath house is generally kept in good order. The campground store is great. It doesn't carry beer or booze, so make sure you have that already if you want it.
If you want swimming pools, Wi-Fi, game rooms, golf cart rentals and people dressed up like cartoon characters, this isn't your place. If you want to relax and enjoy the quiet, read a book during the day, pick up your rod and go fishing in the big pond when you get bored, go to the small pond in the evening to catch your supper and cook it over campfire coals, this place is for you. The trout pond is a great place to try out new flies and rods.
It's only a few miles from Crabtree Falls, but for some reason I've never been there. Still, you're within reasonable driving distance of Waynesboro, Lexington, Natural Bridge and even Charlottesville.