No state income tax in Tennessee. Lots of tax exemptions for retired people in Georgia. My parents moved from Tennessee to Georgia 5+ years ago. They love the lack of income taxes for seniors; depends upon how much you make as a senior. Stay of the metro areas for either and property costs and taxes are pretty low.
Property taxes are pretty low in Georgia. Here in Cobb County once one of the owners turns 62 you can get exempted from the school portion of the property taxes; that's the majority of the property tax. Cobb is a bit close in for cheaper prices and enough land to build a runway though. Maybe in the western most part of the county it might get rural enough for that. Maybe.
I don't know how TN is now on concealed carry, but many years ago a co-worker in Nashville said you basically had to be related to or buddies with the sheriff; could be a city thing. In Georgia it's easy to get a concealed carry permit as long as you aren't a felon.
There is annual property/usage tax on planes in Georgia.
There used to be for cars too, but now it's just a one time sales tax. I don't have a boat, so not sure how those are handled; looks like annual property taxes from a quick Google search.
I've never landed a plane on turf/dirt. So I haven't looked into building a runway. There are plenty of private turf runways around, even a paved runway in the metro area; Stockmar, 20GA. Maybe the rules have changed since all of them were built. If you build a runway and want to let others use it, the state helps protect you on liability:
To encourage landowners to make their lands available to the public for recreational purposes Georgia law (OCGA 51-3-20 through 51-3-26) explicitly shields landowners from civil liability for injuries to persons who use their land for recreational purposes without charge unless the landowner willfully or maliciously fails to guard against or warn of a dangerous condition, use, structure, or activity.
There's a lot less worrying about ice while flying in the southeast. Oh, I've picked it up a few times in the winter, but that's been IFR. Staying below the clouds was an option, and at times my "out".