Please please please do a simple forum search on Charleston. There have been literally dozens of threads just over the past couple of months dissecting Charleston restaurants from every angle, including threads devoted to your very question. As Charleston is one of the most exceptional foodie cities in this country, it would be unreasonable and incomplete to even attempt rehashing recommendations in yet another thread. Happy hunting, and enjoy Charleston!
For an all-around good reference of "best restaurants" for Charleston by a proven palette, go here:
That list is exclusive to all the good restaurants in Charleston, (apart from FIG, Cordavi, and McCrady's, which were named separately as the three best restaurants here http://www.charlestoncitypaper.com/gyrobase/Content?oid=oid%3A23283 psst...I disagree about McCrady's...) but otherwise hits 100% of the other top picks (but no more). Over the years, I plan to eat my way around that list to completion.
In my opinion and by word of mouth, the standouts on that list are (in alphabetical order) - 39 Rue de Jean, Al di la, Basil, Blossom Cafe, Charleston Grill, Cru Cafe, Cypress, Dining Room at Woodlands, High Cotton, La Fourchette, Old Village Post House, Peninsula Grill, and SNOB.
I recommend you try hitting as many of those as you can for your first visit, as you really can't go wrong with any of those.
SNOB is not as good as FIG or Woodlands up in Summerville, or the new incarnation of the Charleston Grill, in my opinion. That's not to say that it isn't good in its own right, but I had a chance to oversaturate my exposure to good Charleston restaurants in the span of a few days, and SNOB is not as good as some others.
As I wrote in another thread on FIG v. SNOB, "Between the two, I think FIG is the better bet. The atmosphere there is wonderfully cohesive and contemporary, while SNOB is a bit too satirical of, well, snobs. I think that's what they were going for anyway, but it comes across as "art deco/italian/buca di beppo" with the faux chandeliers and gaudy parody of high-flying style. It's weird to me. The food was also better at FIG. For goodness sake, PLEASE order the short ribs. If it were possible for heaven to fit in one's mouth, that's how. Best single bite of food I've ever tasted."
Also, if you have a chance to drive 20 min. out from Charleston, I recommend you try Woodlands for lunch. http://www.woodlandsinn.com/dining.cfm One of the best overall dining experiences I've ever had, and anything better than in the city proper. It's one of only 13 restaurants in the entire country to have a 5-star rating from Mobil. Lunch is not that expensive. Two cocktails, two appetizers, two entrees, and two desserts only put us back $70.