You will find many more campground vacancies on the NC side of the Smokeys. Same mountains, much less traffic.
As to timing, you will never find colors everywhere, but you will always find colors somewhere. It's just a matter of finding the elevation that has colors near where you are.
We will go to Whittier, NC 3rd week in October as we always do. Sometimes there are colors in the campground, sometimes we have to go to the top, and last year the best color was on the BR Parkway.
2013 Tundra, 5.7FF, TRD, 4WD, tow pkg
2014 Forest River Cherokee 264
Prodigy II / Equalizer 10K
103 nights & 12,700 miles since April '13