Dave,
Otter Creek Campground @ MM 60 on the BRP has a creek running through it with many campsites near the creek.
All campgrounds on the BRP are on a first come first serve basis.
If Otter Creek was full there is a Yogi Bear campground @ Natural Bridge Station not far from the BRP (exit onto SR 130 @ MM 61) it has a lake and you get to cross an awesome mountain on SR 130.
http://www.campnbr.com/There is also a campground on a small lake @ Montebello, VA (On SR 56 @ BRP MM 27).
http://www.montebellova.com/If I think of any where else I'll let you know.
Also give me a shout, (I'll PM you my cell #) as long as you're in the neighborhood I'll be glad to share some wind and show you around a bit.