+1 on Edmund's Oast... great atmosphere, good food and a wide selection of their own brews and another 20-30 guest taps. Check out the following link from craft beer.com...
One thing to note is that the Charleston Beer Exchange downtown has now closed... it's going to make a sort of a reincarnation though in the form of a huge new bottle shop up next to Edmund's Oast though (CBX was owned by the same guy as Oast)... that's supposed to open in the Spring.
Westbrook is awesome. Close by in Mt Pleasant is Two Blokes. I recommend Holy City and Frothy Beards as well. Charleston has a total of 8 craft breweries unless I missed one.
If you like sours, Westbrook hits home runs as does Wicked Weed in Asheville NC