I don't think you will find a site like that. An RV of any kind costs thousands and thousands of dollars. Even used an RV is expensive! The risks of renting an RV are high. Someone with no experience driving/towing, using the various RV features (believe me, the bathroom in an RV is totally different from what you'd find at home!!!), and such result in a high likelyhood of damage to the RV. Heck, we own a 23 year old pop up camper, and DH backed over a stump last trip ripping off the step! He's a towing expert, and accidents happen.
If you're interested in staying in campgrounds but don't want the expense of renting an RV and aren't into tenting, many campgrounds have cabins to rent. They're bare-bones, but you're off the ground! You provide the linens and towels, your own cooking gear, and the bathrooms are shared.
I grew up camping, and it used to be that camping was way cheaper than hotels. However, camping near any type of tourist attraction is getting as expensive as a budget motel. We're going to Hershey PA this summer. The campgrounds near Hersheypark are almost $50 a night for a site. The Motel 6 a few miles away is $41 a night. We're staying there. There's AC, our own bathroom, and we don't have to haul a 2000 pound camper!