I was raised and lived in Chattanooga for 64 years. Very good place to live. Crime rate is probably below most cities of that size. Property taxes are decent. Housing is about average cost.
Watts Bar is my FAVORITE lake to fish. Spent thousands of days there (an hour from CHA). Smallmouth fishing is great as it largemouth. Lake fluctuates in the winter for flood control (as do most TVA lakes) but main ramp access is still good.
Chickamauga (Tennessee River) is also a great lake. More of a "river run" impoundment than Watts Bar but spits out huge largemouth recently.
As for air travel, Chattanooga or Knoxville both have connecting flights to Atlanta (you have to go to ATL to get anywhere anymore) and Nashville ... but CHA (American Airlines) is now running direct flights to Dallas and other large cities.
Health care is wonderful in Chattanooga. I had by-pass surgery there and the Heart Institute is a great place if you need it.
www.chattanoogafishingforum.com is a great place to browse around for local fishing information.
As for a "remote" lifestyle, the shorelines of the Tennessee River (Watts Bar, Chickamauga, Ft Loudon,etc) are heavily developed but still can be private if you look around. Waterfront property brings a premium price as it does in most areas. We lived waterfront on Chickamauga for a few years and loved it there. On the other hand, country-style living abounds in the Chattanooga area and you are still 30 minutes or so from some great fishing.
Feel free to message me for anything in particular that concerns you. I know that area extremely well.