I agree on Coulter's bridge to Little Johns. That's a nice float and appropriate distance. Access on the Holston and FB is very limited and I believe would require a full day float to get between takeout. Of course you could put in somewhere, paddle up and float back. I'm not much help on access for those rivers though. The Little Pigeon also offers some good float options as well.
"I've got to stop wishin, I've got to go fishin"