Native Arkansan here, been to Memphis 100s of times. When I was young, my mom ran a summer literacy education program in the under privileged delta schools of eastern AR, and the Ramada in West Memphis was our base of operations.
The big shows don't come to Little Rock, went and saw Elton John at the Forum last week. Plus SWMBO's extended family is all in German Town and Millington, so we're there every Christmas and Thanksgiving too.
I miss the old Pyramid, it's a damned Bass Pro now. They used to have amazing touring exhibits, I think they were called The Wonders Exhibits, which were Smithsonian style, audio guided, exhibits on all kinds of stuff like; The Ottoman Empire, The Titanic, Napoleon, The Chinese Terracotta Army, etc. I digress.
Rendezvous is okay, but there's WAY better, less touristy BBQ in Memphis. Central is my favorite, get the pork rinds!
Graceland is okay, the auto museum is better than the house, but I'm not a big Elvis fan.
Peabody is a neat old hotel. The ducks are kind of gimmicky, but if you've got kids they'll love it. I've never been disappointed with their bar.
Mud Island is neat, I'd go when it's warmer though.
The Cotton Museum, and National Civil Rights Museums are both worth a visit.
Sun Records of course, you already mentioned. I recently saw Million Dollar Quartet at our little reparatory theater, now I want to go back.
Sorry I missed this the first time around. If you go back, feel free to hit me up with any questions.