Hey
Off the top of my head:
Bristol Pickin Porch (Bristol Mall) - Various times/dates I think... you could google and call them.
Rheatown Store (Saturday nights roughly 7-10) - Rheatown/Chuckey Tennessee (Google it)
Red Barn - Sciota Road in Unicoi (either Friday or Saturday nights I think... I forget :/)
Fletcher Feed and Seed - Fletcher NC
Feed & Seed - Bluegrass, Old time gospel, non-alcoholic family friendly concert venue and church in Fletcher, North Carolina. , NC.
Bowmantown Music Barn Collins Rd. Bowmantown, TN (Friday nights - a GOOD venue, very intimate)
The Cranberry Thistle - downtown Jonesborough, various days/nights and jams, including old-time
The ones I'm most familiar with are Rheatown, Red Barn and Bowmantown. The people that own the Bowmantown Music Barn are some of the friendliest people I've ever met, and there's food served too!
Welcome to east TN. It's a pickin' heaven. I think there's also a hardware store in downtown Rogersville??? that has jams. Not sure on that one.