Hernando Point is about 30 minutes south and we camp here VERY often. Nice COE campground and I highly reccomend. Clean and good utilities.
The Horn Lake and Southaven campgrounds are less than 1 year old and the Horn Lake has a pool and hot tub.l They both are so new there IS NO SHADE. but they look nice.
You also have the options just south of Memphis for the Tunica casino campgrounds.