Most of the great places to eat that aren't too far away are going to be on Johns Island.
Wild Olive is one of the best restaurants in that area. It's probably about 25 minutes from Kiawah. A reservation might be a good idea. It's not too expensive either.
I don't know if Crave is still on Johns Island, but it's awesome too. It's more of a brunch place though.
Chez Fish is the seafood place to go out there. I don't think it's as good as the places you'll find downtown Charleston or on the Isle of Palms (where I used to live), but it's still good.
And for beers, there's a Red's Icehouse at Bohicket Marina that I used to go to all the time. You'll get better food at other places, but Red's has a great view and cheap drinks and apps.
If you decide to go into Charleston, let me know and I'll recommend two or three places there. Some of the best restaurants in the world.