We normally use interstate thru Chattanooga then get on hwy 11 in ga. It runs along with the interstate. You can side trip to little River canyon if you have time and in gadsden al there is nocolula falls. Both are Nice stops. Hwy 278 goes west from gadsden to Cullman al, where I live. From there take hwy 69 to Tuscaloosa al. Careful on a couple curves on that road they sneak up on ya. From there if you are a glutton for punishment, there is hwy 43. All the way to mobile al.
If you prefer going through huntsville al you can go hwy 72 from Chattanooga into huntsville. It's all 4 lane, but not a bad ride. Hope this helps.
If I'm home I'd buy a meal and ride with ya a couple hours, but I'm always on the road.