Left HotLANTA in 1986; still miss it desperately. There are so many wonderful restaurants there, so many that I remember which are long gone and so many that I never imagined which have become mainstays in my too-long absence.
The first two that came to my mind when you mentioned staying in Buckhead were:
Mary Mac's Tearoom on Ponce De Leon --
http://www.marymacs.com: An Atlanta institution for decades.
Varsity Drive In --
http://www.thevarsity.com: You'll have to see this place to believe it. Not the satellite operations like the Varsity, Jr. out on Lindbergh, but the real deal on North Avenue near the Fox Theatre.
The Varsity -- The World's Largest Drive-in sits on more than two acres and can accommodate 600 cars and over eight hundred people inside. On days of Georgia Tech football games up to 30,000 people visit The Varsity. It sells more than two miles of hotdogs daily, a ton of onion rings, 2500 pounds of fresh cut potatoes, 5000 homemade fried pies, and 300 gallons of chili, all of which are made from scratch daily. The downtown Varsity is also the world's largest single outlet for Coca-Cola.
Neither of these qualify as "fine dining", but they are North Georgia legends that you really should check out for lunch, if you can.