There is a nice museum with a laughably old film (but still worth watching), which is a good starting point before you walk out to the fort. There is more to explore here than at Fort Sumter as you snake around through the various magazines and gun emplacements. Like Sumter, there is a more modern battery plunked on top of the old fort, part of the defenses arranged at the time of the Span-Am War.
A boat-tailed grackle and Charleston harbor
Checking out one of many magazines.
The dirt piled up protects the magazine from incoming projectiles.
I liked this site more than Fort Sumter because you don't have to take a boat and fewer people are to be found here. There's also more to see!