Don't discount some of the northwest state parks, up I-75 north. Leaf color in that area is pretty good from the 1st-2nd week in October thru the 1st week in November.
Red Top Mountain SP is on Lake Allatoona, at Cartersville. Red Top is one of the most popular SPs because it is close to Atlanta, so you better get reservations ASAP if you want to go there. Farther north is James "Sloppy" Floyd SP--its a smaller park, in rolling hills. Another good one is Cloudland Canyon SP, near Chattanooga.
I would not suggest Fort Mountain SP. It's a fabulous park but you have to tow about 8 miles up a really steep, curvy road. Not my cup of tea and maybe not yours.
Also, look at some of the COEs. Our favorite is McKinney COE,which is a couple miles off I-75 north before you get as far as Red Top. It's a large campground with lots of woods. There are some other COEs around Lake Allatoona but I don't like them as well. Definitely not a fan of Old 41 COE. The sites are narrow and a lot of them require backing your rig all the way down the hill almost to the lake. Yikes! Too scary for my taste. Payne COE is my least favorite--they lost thousands of trees to pine beetle blight about 12-15 years ago and they've never recovered. Most of the campsites are out in the bald-bare sun.
Good luck to you. Just a heads up, in case you don't already know--you cannot reserve a specific site in the State Park system. You reserve a category of sites and when you get there, its first-come-first-serve for that category. Which means if you pull in at 8pm on a Friday night the pickings will be slim. You can reserve specific sites at the COEs.
ETA: I forgot about one of the best state parks--FDR SP! It's off I-185, very near Callaway Gardens in Pine Mountain. It's a fantastic state park and very popular.