Yeah, if you go to Savannah, make sure to visit the Bamboo Farm and Coastal Gardens.
Lots of bananas there! In fact, there's sort of a mini-plantation area there. GATrops, a member here, could probably tell you more. Large hardy palm collection there also, sponsored by the Southeastern Palm Society.
Valdosta is a nice area, lots of hardy palms around the area, plus a theme park whose name escapes me right now.
Athens is home to the
State Botanical Garden of Georgia, just a short drive from Atlanta.