[Anaraxes]

For Georgia, you might consider Folkston or Waycross, as those give you access to the Okefenokee Swamp.

Cordele, Georgia, is notable for having its own Titan I nuclear missile, if that's useful for a plot. (The real one is of course demilitarized, though it was an actual missile, retired. But fiction likes to exaggerate, so maybe someone kept the warhead -- you know, just in case It ever got out.) Fails the isolation requirement particularly hard, though, as it sits right on Interstate 75. As others have said, no town in Georgia is truly physically isolated.

For more of that Twin Peaks feel, you'd want to be in north Georgia, so you have more trees and mountains. Rabun Gap, Tallulah Falls, Pine Mountain, Ellijay, Blairsville. There are quite a lot of wilderness areas / national / state forests in the northern part of the state. You'll have more luck with physical isolation up there, at least on a local scale. Though Atlanta's never more than an hour or two away. A couple of convenient highway closures could go a long way.

You might also go with Darien. It's got some history, once being a relatively important port, but that's long gone. You have a lot of trackless swamp along the Altamaha River, and the coastal sawgrass and barrier islands. I-95 is nearby, but that's just people blowing by at 80 mph, not getting on or off the freeway here, headed for Savannah and points north, or Jacksonville and points south, without giving this sparsely-populated region a second glance, much less stopping. So you might be able to use that to reinforce the isolation by contrast, and make it a metaphor for the world having moved on and forgotten about the Thing They Were Not Meant To Know in their midst.