We just returned from a camping trip to both cities. While camping at Hunting Island State Park in SC we took a day trip to Savannah. It was rainy but we walked around the waterfront area, visited small shops, got a bite to eat and just enjoyed the area. We rode out to Wormsloe Historic Site which was very pretty and worth the ride. We did not pay to go onto the grounds, just took some pictures of the road lined with 400 live oak trees.
We changed campgrounds mid-week to Edisto Beach State Park and went into Charleston for a day as well. You have already gotten some great suggestions for Charleston, one activity not mentioned and something we did and enjoyed immensely was taking a cruise on "Fate" a charter sailboat that leaves from the City docks. After spending the day walking around the Battery and Market area it was great to board the boat and sail around the entire peninsula seeing the city from the water. We sailed under the Ravenel bridge, past the old fort in the harbor, Fort Sumter and just about into the ocean, this was everyone's favorite activity of the entire week. Great crew, beautiful boat and a unique experience!