My family does lots of camping throughout the year ... and I would show up a day early at the campsite (maybe like late afternoon). That way, you can relax a little bit and get totally setup, and then you ought to be able to "come back" to the camp at any time day or night, as the site will already be yours, regardless of the office being open or not. Most sites (especially a state park) run about $9 - $18 per night, and surely that is MUCH cheaper than a hotel.
However, if staying in a hotel becomes an option, then by all means there are TONS in the area of SFOG:
http://www.georgia-info.com/sixflagsovergeorgia/
http://www.sixflags.com/parks/overgeorg ... index.html
Hope this helps ....