Savannah is a gorgeous city with tons of history. We like to bring bikes and just ride around the city, look at the beautiful houses, the trees and Spanish moss, the gorgeous squares and open areas.
River Street is a pretty cobblestone street right along the Savannah River, lots of touristy shops and an open air market down there. A couple of blocks inland is nice shops and restaurants. Best pizza down there is Vinnie Van Go Go's (cash only). Its a great place to walk around or ride bikes around. Very pedestrian friendly in that area.
Forsyth Park is very pretty too. They have a huge playground area for kids, lots of open areas for lounging or playing ball. If I remember correctly they have a small live music in the middle. It is most well known for a beautiful fountain there too.
Its a great city to just go and meander around. We go there almost every February on the way to Florida. Its a beautiful city to visit with no real plans... just show up and enjoy the area.
Hope you have fun!!!