OP should consider Black Rock Mountain State Park. This is East of where they intended to go, but the park is the highest elevation park in the state, the campground being something like 3500 ft. Its relatively cool in the summer. Nice campsites with electric and water and there are two restroom/shower houses.
The park has good views, and a couple of trails to walk, and you will find easy access to two or three large "Georgia Grown" food and produce markets along US 23. The Foxfire Museum and Heritage Center is located right in Mountain City, where the turn off to the park is. If you are not familiar with the Foxfire series of books, Google it, this is the origin of those books.
Going north is the town of Dillard and there is a restaurant called the Dillard House, which is rather famous for its food and service. Franklin NC is just a short distance up the road and you can visit the Gem and Mineral Museum in the old Jail house.
Also on US 23 south of Clayton is Tallulah Falls State Park which also has a campground is a very scenic area.
The only issue with Black Rock Mtn SP is the 7 or 8% grade for a mile and a half or so up to the park. The campground is situated along the top of a ridge, and one site in particular I recall, if you make a wrong turn out of the camper door you are in for quite a drop. Generally the sites are very nice and there is a lot of trees and vegetation around.
If you are staying at more than one GA park this year, consider a Friends of Georgia State Parks Membership. For $65 you get one annual pass and one free night of camping, For $90 you get a annual state park pass, and two nights of free camping, and for $105 you get three nights of free camping and two annual passes. The annual passes allow you to enter any GA park without paying the day use fee.
https://friendsofgastateparks.org/node/1076Charles
