I second the recommendation of SNOB if you want a sophisticated dining experience in the cityof Charleston. Robert's near the city market has good dining and an owner who seranandes you with his operatic voice.
If you're adventurous, I'd suggest heading out Highway 17 North (the Cooper River Bridge) about 15 miles to the SeeWee Restaurant in Awendaw. This is the peasant cooking of the low country done in outstanding fashion.
Another interesting place located on Edisto is the Old Post Office, a really great upscale place that focuses it's menu on the fresh meat, fowl fish and vegetables that can be found in that fertile area. To get to Edisto, take 17 South (The Savannah Highway) to Highway 130. 130 will take you right into Edisto. Your friends will think that you're an old time local if you know about this place. I love the shrimp and grits as well as the duck with rasberry coulis.