Going north to south there is no good way to avoid Nashville. The only alternative that comes to my mind is to jump on SR 155, Riley Parkway southbound. It is a real good multi-lane highway but you will be forced to exit that road where it intersects with I-40 near Nashville International Airport. From there, take I-40 west to I-440 then to I-65 south.
During rush hour all of those roads will be jammed with cars and the only real way is to go on Sunday or after rush hour. If you are stopping for the night well north of Nashville up in Kentucky and can exit I-65 and get to US 231, then you could take it south to Lebanon, TN and use SR 840 and totally avoid all of Nashville. We've driven US 231 several times when we go up to the Elkhart, Indiana area and it is a nice drive. And SR 840 is a wide open highway.
2012 Tiffin Allegro 34 TGA
Ford V-10 22000 lb chassis
Brake Buddy Advantage,