We stayed in Savannah for our anniversary this year. Great little town.
We stayed at the Avia, which is very nice, somewhat contemporary, in a fantastic location. We only used the car a few times during our stay and walked everywhere else.
Favorite places we ate:
The Olde Pink House by far our favorite. The Cheerwine BBQ Chicken Sliders on the appetizer menu is one of the best things I've ever put in my mouth. Their Strawberries Romanov Chocolate Cake is amazing as well. Beautiful old house, great service. We ate their twice - once upstairs in the formal house and once downstairs in the old tavern setting - you swear Paul Revere and Ben Franklin could be over in a corner gossiping about the British.
Goose Feathers - a little cafe with great sandwiches and such on Broughton Street near Ellis Square.
Huey's on the River - biegnets for breakfast on the riverfront.
Wiley's Championship BBQ - south of town technically and a 20 minute or so drive, but the best beef brisket I've ever tasted - melt in your mouth - small place in a strip mall, but among the best BBQ I've had and I love my BBQ.
Walk around! Savannah is very, very walkable. Not once did we feel the need to take a trolley, but you can certainly do so. We walked almost everywhere. It's not as big as you may think. The whole town is full of amazing old mansions and houses and churches and squares and oak trees, etc.
Visit the old churches, museums, shops, etc. Tour some old houses (such as the house where Midnight in the Garden of Good and Evil took place).
Walk through the cemeteries. Drive out to Bonaventure cemetery for a few hours and walk around - the place is huge.
Visit the Savannah Bee Company store if you like honey.
Leopold's Ice Cream shop is a well known little place on Broughton Street.
Plenty of options for Ghost Walks and Pub Crawls if you are into any of those things, too.
Here's a bunch of photos I took if you are interested:
http://www.flickr.com/photos/penglynns/sets/72157624763818978/