Just rode from Atlanta to Nashville and back a few weeks ago. (Actually went to Lebanon, skirted Nashville, then over to Franklin.) Plan on five days of riding.
Went up through GA and came back via AL. (725 miles). Pdlamb is absolutely right about 278/431 in AL. I found riding on it stressful, if not down right dangerous. I definitely recommend the GA route.
I took the Silver Comet to Rockmart, Rockmart to Lafayette , Lafayette to Tracy City, Tracy City to Murphreesboro, and Murphreesboro to Lebanon. You should be able to fill in the route details with Google maps from there, although it did mis-direct me heading to Lafayette. (Hint: stay on the Dalton road out of Rome.) Otherwise, ask the locals. they know the roads.
The prettiest parts of the ride were riding through "The Pocket" into Lafayette and up 193(?) out of Lafayette into St Elmo, Tn. St Elmo was an oasis with both a coffee and buritto shop.
US 41 turned out to be a good route out of St Elmo all the way to Murphreesboro. (I-24 picks up all the traffic.) Expect some climbing out of St Elmo around Nickajack Lake, but you'll be rewarded with a great descent.
After crossing the river, you'll have to side-track through Jasper because, as I understand it, 41 merges with I-24 to go over Monteagle. Coming out of Jasper is where you'll climb the Cumberland Plateau. Things get flatter after that.
I found three campgrounds. 1.) two or three miles before hitting Rockmart just off the Silver Comet (water, and outhouse. Questionable on the shower); 2.) about eight miles past Rockmart on the trail (primitive) 3.) a state park a few miles after climbing the Cumberland Plateau out of Jasper, which is about eight miles before you hit Tracy City. Otherwise I stayed in motels in Lafayette and Murphreesboro.
I stayed at the Jackson(?) downtown in order to avoid going toward I-24 for the chain motels in Murphreesboro. The attendant was behind plexiglass, but the room was clean and cheap. I felt safe enough.
I veered off 41 after Murphreesboro to go to Lebanon, so you'll have to figure it from there.