I live in a relatively small town in south Georgia - Tifton. And, while we have some local authors (Brenda Sutton Rose and Janie Hopwood, among others, to my knowledge we do not have any fiction books set in Tifton itself.
However, I have seen Tifton mentioned in a couple of Karin Slaughter's books (Faithless and Skin Privilege come to mind) and, I have to admit, it always gives me a thrill...lol. It has also been mentioned in John Sandford's Neon Prey - you can read about it in an interview with the author!
In Georgia itself there are way too many to name. A few that come to mind:
All of Karen Slaughter's books
Gone With the Wind by Margaret Mitchell
Midnight in the Garden of Good and Evil by John Berend
Cold Sassy Tree by Olive Ann Burns
Between, Georgia by Joshilyn Jackson
The Night the Lights Went Out by Karen White
There are too many more to name...and I'm out of time!! :-)