Have done Savannah twice in recent years...and you will need to rent a car to get in to Savannah itself. As the previous posts suggest, Savannah is approx 20 - 30 mins from the airport.
Several hire car companies are adjacent to the carousels... Hertz, Avis, Alamo etc.. though it may be a good idea to pre book a car before you leave home!.
And dont forget to check out River Street!