Another vote for the Natchez Trace Parkway, but I would route myself through Nashville (where the parkway starts) and make Nashville one of my destinations, two or three days there at least, for all of the Music City and historical Tennessee points of interest.
From SW Michigan to Nashville is likely taking you through Louisville (and bourbon country for maybe a distillery visit), then Bowling Green to see where the Corvette Museum fell into a sinkhole. Might even take you through Indianapolis, and if you do, you want to see the Speedway Museum out in Speedway Indiana.
You will be going through Houston between New Orleans and San Antonio. I visited Houston often on business, and towards the end of my wife's life the Texas Medical Center. My experience, I think it is worth a visit to see the Space Center, and see how a multicultural city works when there are few rules constraining how and where people choose to live. But if you are from Southern California, what's going on in Houston is probably no big deal, kind of the same lifestyle but without the beach and without the water shortage constraints.
Tom Test
Itasca Spirit 29B