Camping southwest of Nashville/Harpeth river/Natchez trace recommendations

I have to travel to Nashville end of February. I’ve always enjoyed the Natchez Trace for a relaxing drive and haven’t been on it north of Tupelo. I’m trying to find a place to tent camp, but a lot of places don’t offer camping even though it’s a state park. Also, apparently they stock the Harpeth with rainbow and would love to fish it while in the area. I don’t see any camping around Harpeth though.

Does anyone know any good locations in that area? Preferably with showers.