You must go to River Street and the Historic Area. Spend a few days there. Old days and pirate stuff. Nice restaurants if you like seafood, Tubby's in Thunderbolt. The Tubby's on River Street is okay, but the original is much better. However, the parking lot is dirt, so be careful on a bike. If you don't feel like walking, there are many tours you can ride and let the guides explain the sites. Nice and relaxing.
If you go out at night, be careful and try to go with a group. Stay out of the dark alleys. Crime, it sux.
If you're into playing music - check out Rody's - best music store I've ever seen. I used to slip down to Savanah when I was stationed in Charleston, loved the city but I was a LOT younger then. River street and the Southern charm of the old part of the city were high points. So Antebellum!
Don't pass up the opportunity to tour Savannah on the Segway. It is a hoot. The tour office is in the city center area. We parked our wing at the visitor center and walked the entire downtown district. There is parking along some streets but the visitor center was always there.
We stayed in the historic area will be taking another trip down this year. The trolley tour is worthwhile and brings the area history all together. The town is well worth the trip, especially when you learn some of that history.