We live south of Memphis in northern Mississippi. I like the Hernando Point COE campground that is between Hernando and Coldwater, MS. It puts you about 22 miles south of Memphis away from the city. Campground is set on a lake with lots of trees.
Your other choices are Tom Sawyer campground in West Memphis, Arkansaw which is highly recommended by many. There are several RV parks in Southaven, MS that would work for you also. These are typical RV parks, packed tight with full hookups.
You will find a lot of good riding in Arkansas - one of our favorite places to ride. Keep the bikes in the trailer in Memphis - very flat and not too many curves!
