I have no first-hand knowledge of most of these groups, but here's what I find online:

Garden Thyme Herb Society - no official contact info online.
If you're interested, contact GardenWeb member evasage for more email. You should be able to email her through her GardenWeb member page. Eva's super nice and might also be able to tell you about other local groups.

Ken-Ten Iris Association (Dresden, TN / Earnie Royal, president / 270-489-2819) - local American Iris Society group
I can hardly believe that the Tri-Cities doesn't have an AIS club in that area, but it appears that this one is the closest. If you are into iris, you might consider starting a club in the Tri-Cities area. I bet there'd be plenty of interest.

Mid-Appalachian Bonsai Kai (Kingsport / Anita Bausman at 423-239-7602) - local American Bonsai Society group

Tri-Cities Daylily Society (Kingsport, TN / Dennis Hall, president at 423-288-7040) - local American Hemerocallis Society group

Shady Oaks Garden Club (Johnson City, TN / Cindy Hintz at 423-282-9106)
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I didn't see any local groups associated with these groups, but you might consider starting one:

African Violet Society of America
American Daffodil Society
American Hosta Society
American Rose Society
Cactus and Succulent Society of America
wildflower groups
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There are also other groups that are somewhat associated with plants and gardening, like:

Bays Mountain Park Association
Bristol Bird Club
Friends of Roan Mountain
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And, of course, you are cordially invited to attend the East Tennessee Plant Swaps. Look for info in this GardenWeb Forum closer to swap time (usually one in spring and one in fall).

This group looks like it is fairly close to you. You might want to check them out. It's a new group that was formed in September.

Here is a link that might be useful: Dungannon, VA group

The largest club in the area is the South Applachian Plant Society (SAPS) Their website listing meetings etc is SAPS.US

Additionally, check with the extension agent (Chris Ramsey) located in Blountville.

Here is a link that might be useful: South Applachian Plant Society Web Page

Hey, there is a small community garden at Carver Park in downtown JC. Lovely crowd. Want to meet us?

Thank you, everyone, for the wonderful responses! I'm sorry I didn't respond earlier, but we've had some nasty bouts of flu, bronchitis, and other assorted illness. Looking forward to puting winter behind us, and being able to open doors/windows and freshen the air again!

Thank you, again! :)