You really can't go wrong with Meeman-Shelby. It is so damn close to Memphis that while you won't feel like you are near an urban center, you benefit from its proximity. I very much appreciated being able to site see and camp during our brief overnight here.
The campground itself is tucked away deep into the Meeman Shelby State Forest and offers a pleasant amount solitude even though the sites are fairly close together. We watched an super long RV struggle to back into their site, so I wouldn't recommend this campground to RVs that require pull through sites.
Not all sites are suitable for tent campers. I would call ahead to ask what sites to consider if booking online, or just show up. There are a lot of sites here and you'll find something.
The campground is not terrible even, so be prepared for that.