There are a lot of great places depending on your budget. Downtown, I really like The Peninsula Grille ($100+ for two). A little less fancy but as good or better is SNOB. Fleet Landing is good and right on the water, near the cruise ships. It's more casual then the other two.
I prefer to eat in the East Cooper area (Mount Pleasant, Sullivans Island, Isle of Palms). Food is usually better. Prices are better. Parking is easier. Some favorites are:
Yo Burrito (inexpensive casual dining in Mt. Pleasant)
Sticky Fingers (ribs and bbq, just over the bridge in Mt. P.)
Vickery's (I think it's the best on Shem Creek, especially for lunch)
Benito's - (Mt P. - in Town Center, they may be closed or moved due to lease issues with shopping center)
Sullivan's (great casual on Sullivans Island)
Uno Mas (slightly upscale Mexican in Mt. P., not expensive)
Poes (upscale burgers on Sullivan's)
Long Island Cafe (Isle of Palms)
The Mustard Seed (Mt. P - this is where we usually take friends who come to visit)
Long Point Grill (Mt. P. great lunch)
The Wreck (on Shem Creek and many people think it is the best in the CHS area)
Morgan Creek Grill (Isle of Palms, great Sunday Brunch)
I write up reviews on my blog sometimes -
East Cooper - Paradise this side of Heaven