Just walking up and down the Battery and outlining streets is still the best.
Don't forget to ride (or drive) down to Isle of Palms.
I prefer Sullivans Island to the Isle of Palms - beaches less trodden, more charm. I do remember thirty years ago when a large part of Isle of Palms was wild scrub - Goldbug country.
Officers' Row, on Sullivans Island, has gorgeous houses, lush trees. Fort Moultrie is nearby - easier to get to than Fort Sumter if you don't have much time.
Yorktown if you like aircraft carriers.
One of the plantations if you like gardens.
Eat seafood at every meal.