Call the Caverns it's at the foot of the mountain close to Pelham. They might have a place you can camp.
I camped out next to a lake at Sewanee back when I was in college and there seem to be very few students at the school right now. I don't know if they frown on that or not these days though. Cheapest rate for Smokehouse is on Hotels dot com around $50 weekdays.
Thanks! Your answer is awaiting moderation.