Charleston Muni is a fun track. I only played nine holes, but I remeber some fun golf. Supposedly there is Raynor influence, and I remember one Raynoresque green site. For eats, Reeves offers the best barbeque in town, south of Charleston.
The Ocean Course is a lot of fun, but not my favorite, seeing as i only played it once, and that was a couple years ago. Probably worth the cash.
I did visit Briar's Creek on the Kiawah River, but did not play. Very cool place, totally isolated (the sign for it doesn't have a name on it!!), but the setting is awesome. Recommended if you can get on.
Most of my golf in Charleston was played at Seabrook Island, just South of Kiawah. The Willard Byrd course is fun, nine holes in the woods, nine in dunesland/marshland, with some strategically interesting holes. There is housing, but the course is definitely walkable. Not great, but certainly a fun place.