Yes, your Florida concealed carry license is valid and recognized in Georgia, in fact Georgia recognizes ALL States licences that recognize the Georgia License, which is most of them. Now, unless there is a notice for no firearms on premises (rare but some do exist)you are not in violation if the establishment sells more food than liquor or beer. In other words, just because the little bar sells hamburgers and frozen pizza along with the beer does not qualify it as a restaurant, and there you would not be legal.
My experience has been any time I have an official conversation with any LEO, I think it is a good idea to mention that I am licensed to carry and am doing so. I have yet to have one even ask to see the weapon, or the license. I have been told by several, the fact I volenteered the information made them feel at ease in my presence.