Eugene, Woodfire and Floatway are all excellent.
Old School "Tea Room" fried chicken and meat and three can be had at Mary Mac's on Ponce in Midtown. Or try Collonade on Cheshire Bridge for the same.
If you don't mind a longer cab ride or MARTA trip, head to Decatur for either Cakes & Ale, low-key, local farm to table restaurant. Or try Watershed, Scott Peacock's excellent Southern "gourmet."
Dogwood is new, have not heard anything one way or another. Southern, local and farm-to-table are how it's positioned. Southern end of Midtown on Peachtree.
Restaurant Eugene...north side of midtown but a quick cab ride.
Some may suggest South City Kitchen but the food is hit or miss.
At Eugene the food is outstanding with a mellow atmosphere. And the mixologist is fun to challenge. He'll make you whatever you like to fit your meal, or pick some good wines as well.