I'm pretty much smack dab between Nashville and Memphis, west of Jackson, TN...which is the home of Carl Perkins. It's probably worth a short stop in Jackson for the Carl Perkin's 'museum', since you are more music fans than lovers of great scenery. That's in the more eastern part of the state.
Sadly, I had to shut down the still. The mash got infested by boll wevils. While they do provide protein, they tend to make the whiskey taste like a cross between Dr. Pepper and Lemon-lime gatorade. OK for me, but impossible to sell.
I can't offer you accomodations, since I'm reduced to living with someone else at the moment, but if our schedules permit, I'd be pleased to meet you for a meal or a rest stop in Jackson. I know all the mediocre restaurants there. Let me know, and I'll PM you contact info. Actually, coming 'here' is not too far out of your way. It might be good to get off I-40 for a spell and cruise through some rural America. Up to you.
Have a great time, regardless.
In Memphis, visit the Peabody Hotel in Downtown. Stay there, if you can. Beale Street is kicking--all of Downtown is so much better than when I lived there. Much of the rest of the City is typical urban and suburban sprawl with only spots of Character. Downtown is the place to stay if your budget allows. There are other 'sights' downtown, and you might get lucky and be there for some show or event. Of course, the River is down there, along with Mud Island, the Pyramid, etc. They had some major flooding recently, but as far as I know things are back to more-or-less normal.
Sun Studios is nearby on Union Avenenue. As far as I know, they are still open for tours...verify that. It's reputation far exceeds the impressiveness of the structure and the neighborhood, but sounds like you'd enjoy seeing where 'it' all began.
Don't be averse to driving further down into Mississippi for a view of the hard-scrabble cotton country where most of these guys (and their African-American musical forebears) came from. Depends on how 'rootsy' you want to go.
Drive carefully.