I can only speak for the Savannah area, as my sister lives there. I would go to the old riverfront. It is a tourist area with a lot of little shops. Very little parking, so you may have to park an walk a little. I also like just driving around the old city, around all the squares, and seeing all the trees overhanging the streets. Just be careful of the traffic lights, as some are hard to see in that area.
The old downtown area is right on the riverfront, downstairs from the street running through that area.
If you or your kids were involved with Girl Scouts, there is Julliet Gordon Lowe's (the founder of the Girl Scouts) house downtown.
I second going out to Tybee Island. Stop by and climb the lighthouse. On the way out or back you can stop by Fort Pulaski. Not a huge fort, but we enjoyed exploring it.
There are several other old house tours you can take in Savannah. My sister works at the Jewish Temple and they give tours there too.