MGD,If you have about two hours, you might want to try the Martin Luther King Museum on the site of the motel where he was murdered. I tagged along on a guided tour last February and was duly impressed.
Also, don't miss Corky's Barbecue. They call it the best BBQ in Memphis and I am a believer. If you are a vegan, of course, skip it. I went back a second time (not for seconds).
Sun Studios is so musically historical, and I love to say I've been there. Don't be expected to be overly impressed. There is not much there, there. It's an office, an acoustic room, and the sound booth (which you can only peek into). I was impressed how much was done with so little.
Roger in Baltimore