Jekyll is nice. In addition to beaches there is the old
Jekyl Island Club. The linked site has a pretty good overview of 'attractions' along the coast. For a less developed island off the GA coast, go to
Cumberland Island.
I second the Savannah recommendation. A beautiful old city!
Also on my 'don't miss' list would be a canoe trip through the
Okefenokee Swamp (on the GA/FL border). But, that would definitely depend on the time of year (not in August!!) & your personal interests.
Are you wanting to see all of GA or just along the coast?