Where are you visiting in Charleston? I grew up there. I don't remember that there are any homebrew shops in the city. You might want to check out Coast Brewing Company
in North Charleston. Its new, and Ive never been there, but I think they might have a shop. I think with current laws in SC, you can't taste beer at the brewery though. The Palmetto beer is easily aviailble down there, but its not the best. They cater to the tourists who think they are getting something special because it says "Charleston" on it. Their Pale Ale isnt bad though.
You should also check out the Charleston Beer Exchange
. Its a bottle shop with an incredible selection. They usually have stuff from Coast on the Growler station too.
Mellow Mushroom located on King Street in the city usually has a great line up of beer on tap. Its not beer related, but I highly recommend eating at The Fat Hen
on John's Island. Its a little out of the way, but it has absolutely incredible food. If you are there on a Saturday, visit the farmers market on the corner of Calhoun and King in the city.