After you finish visiting Charlston (and there is a LOT to see, there, too) you might try finding the Magnolia Plantation and Gardens up on the Ashley river - Worth the side trip.
Many ways to get to Savannah, both fast and slow. The best slow (non-Interstate) way is to travel down SC 17 to Garden Corner and then SC 21 down to Beaufort, which is a very pretty, smaller version of Charleston with lots to see, like the planter's mansions to the East of Carteret St. Take the horse-drawn carriage tour. The Penn Center in Frogmore out on St. Helena Island is worth the trip but out of the way a bit.
Take SC 170 out of the west side of Beaufort to SC 17 and into Savannah over the Hutchinson Island Bridge and find your way to the tourist center on MLK Blvd. Take the Trolley Tour of Savannah (it's worth it). You can get off and on at any of their stops. Drive the Roadster around the parks (there is a park on every other block in the historic district.
Enjoy the trip!