It's 550 miles alonf I 40 from my place in East Tennessee to GailA's in Memphis. I wrote in this thread above about the October leaves. I live in the foothills of the Great Smokies where the color changes are gradual over a period of weeks. October is also Football Time in Tennessee. Knoxville is transformed by 100k fans out of their minds with the Vol feaver.
If you like the heavy duty tourist attaractions as in Pigeon Forge/ Dollywood and Gatlinburg it doesn't matter much.....they'll take your money all year long.
My personal favorite time is April. I'm a wild flower man and that is the season of most flowers and best overall displays.