Been there twice, once by cruise and once driving.
I think it is a walking town, however I walk a lot. In a city like Charleston if you don't walk you miss a lot. There is a lot to see.
Some of the historic houses offer tours, I think these can be booked in advance. I would recommend at least one house tour.
I would do a general internet search for walking tours of Charleston. You can do a self-guided one or there are tours that are led (either through the cruise ship or book your own.
People also take carriage rides.
The food is also very, very good (however I thought it was a little salty). The restaurants do get busy, reservations are highly suggested and should be made well in advance.
FYI, the NPS does a boat ride to Fort Sumter, I've done it. Unless you are a really big fan of civil war era forts not sure it is worth it given you will probably have time constraints. This can be booked in advance.
The historic city market is worth a walk through and near where the ships doc. There is also a more upscale shopping street.
Also, nice to see is the pineapple fountain in the waterfront park.