There is a lot to do in Charleston. My kids love exploring the Yorktown aircraft carrier in Mt Pleasant. The aquarium is decent and I heard they just reopened the theater next door (used to be IMAX but they show regular movies now too). Walking through the "slave" market and watching the ladies make the sweetgrass baskets is fun. Boone Hall Plantation can be fun if not too hot (not sure what they're growing now, but it is blueberry and peach season). Bubba Gumps (based on Forrest Gump) is a neat, fun place to eat. Charleston has lots of good eating places. Over the bridge in Mt Pleasan is Shim Creek with lots of neat places. In the evening you can watch the dolphins hang out while the fisherman clean their catch. There are beaches, Ft Sumter, haunted tours, walking around the Battery, and the Pineapple Fountain to check out too. The park district also runs a few water parks ie Whilring Waters, Roaring Waters and other around the Charleston area.
Have a great time!