When you go to Memphis, go to Beale Street downtown. In just a few blocks you will find several blues clubs. There is also a Blues Museum in Memphis you may find interesting.If you get hungry, I can vouch for great "ribs" at Corky's. They are not downtown, but their ribs are worth going out of your way.
Of course, Sun Studios is in Memphis. There is not much to see there (just three rooms), but if you want to walk on hallowed linoleum that's one place to go in Memphis.
Big RiB