Would the Archives have information on the names of my great-grandparents' parents on my Mother's side and my Dad's side? I want to trace both family lines as far as I can.

Cynthia, use their Ancestry resources. Must visit and get registration card. Good luck

First, your ancestors names you're searching for could be found here if they all lived in GA. Look for them in census reports (every 10 years; latest one accessible is 1940), land deeds, tax digests, jury lists, etc. I've been able to find most everything located at the Archives on familysearch.com. Go online and create your account then watch a YouTube video on how to use the catalog to search for anyone anywhere.