My wife teaches 8th Grade and we do Charleston every year with the kids, here is what I recommend:
Ft. Sumter: The original is there, but only the bottom Tier and a lot has been covered by Spanish American War Battery Huger, which is interesting in itself.
Ft. Moultrie is even better I think, you can see examples of 150+ years of coastal fortifications. From he AWI to WW2.
Patriots Point: with CV10 Yorktown, Destoyer USS Laffy (which is presented very well) and the Submarine USS Clagamore, which is due to be scrapped, so get there soon!
Take a Ghost tour at night, they are fun and will get you to the main highlights in the city. My wife and I think the ghost part is a load of rubbish, but you get good stories and folklore usually.
Also highly recommended:
Boone Hall Plantation: Well preserved Slave Quarters and a very good presentation on Gullah Culture with a great story teller.
Charlestown landing: The site of the original colony, with a well presented museum, reconstruction of the settlement and reproduction coastal trading ship
Unless you like crowds, avoid The Market down town (FYI it was never a slave market, most of that was in the street in front of the customs house)
The Battery and Rainbow row are must sees, wear comfortable shoes.
There are several more plantations that are worth a visit. The aquarium is nice too.
Enjoy your trip!
