There are two reasons to stay in south Memphis [1]: the airport and Graceland [2]. But even if you are keenly interested in either of these places, you should think twice about staying in this part of town. With strip malls, seedy neighborhoods, and lots of mediocre chain hotels, there is not much to recommend it.
Links:
[1] http://www.moon.com/destinations/tennessee/memphis
[2] http://www.moon.com/destinations/tennessee/memphis/sights/south-memphis/graceland