The same group that plans the Chick-fil-A Bowl plans the Kickoff Classic. You can find RV parking info at this site once it is updated -
www.cfack.com
For last year's site and info, just click through to
http://www.cfack.com/HOME/tabid/36/Default.aspx.
I live in Atlanta so we don't take the RV down for these games, but they do have one paved lot for all RV's. I would suggest checking the site frequently to see when they post the information because once it gets posted, the spots are likely to go fast. Once those are gone, there are no other sites that I'm aware of anywhere nearby.
You're within walking distance of the aquarium, the coke museum, centennial park, Stats (a great sports bar) and a couple of restaurants so there is a little bit to do during the day if you arrive early on Friday. I wouldn't be out walking around after dark around the parking lots or the dome though. You'll want a car or taxi to go out a night.