Everyone always recommends Elizabeths's on 37th. It is a very nice special occasion type of place. I personally have never been there but have read and heard several people who swear by it. I want to go...someday. :)
Georges on Tybee is a great spot as well as The New South Cafe - which is located in Savannah on the way to Tybee Island - great food, upscale dining (at dinner, lunch is more casual but still wonderful). Check it out!
I haven't lived there in several months, but I really enjoyed Alligator Soul. And if you're looking for an evening downtown, it's easy walking distance to many other cute bars and places for dessert on Broughton Street. http://www.alligatorsoul.com/