Texas publishes a guide to the public campgrounds in that state. Think it is from the highway dept, not sure, I pick it up at he welcome center.
I've not seen a guide as comprehensive, for other states. Private efforts depend on users reporting them and keeping info up to date. Our city had a RV park on the river near the edge of town, shut it dow permanently when it became meth lab central. Cost of law enforcement outweighed any possible benefit to city of giving visitors an almost free place to stay.