I did a road trip around the USA, but it was in 1991 so things may have changed. It was a bit of a musical pilgrimage so the first tip... I had a load of tapes (well it was 1991) so I could listen to the appropriate music in the appropriate place... like "Sweet Home Alabama" in Alabama (yes, I know they were Floridians, but it pleased me), Mellencamp in Indiana and so on. It's also worth tuning in to the local radio stations, but they are a bit parachial so fade in and out quite quickly. But it's great driving down a long empty highway with American rock blasting out. But keep to the speed limit while you're doing it...
I was a bit underwhelmed by Nashville, but that might have been me... I've got far more into country music since then. Memphis was great and there is nothing like Beale Street at night. It's also worth a visit to Graceland, even if you're not an Elvis fan.
Overall.. it was a fantastic trip... and it will stay with you forever.
Another tip, hotels have to give you special cheap rates if you phone ahead, rather than just turn up (in 1991, at least). There is usually a Tourist Information shop on the Interstate just after you cross a state line... I used to stop at these and get them to book my room ahead at wherever I was going. Maybe you can still do this.
Have fun... and don't get too drunk in Bourbon Street... the cocktails are like rocket fuel and come in pint glasses.