As a local, our favorite dinner combination is oysters Moscow and cocktails at The Ordinary followed by dinner at Halls Chophouse. At Halls, if you can eat a serious piece of meat, I recommend the bone-in filet mignon. It isn’t on the menu or on the standard meat tray, but they almost always have it. Ask for it Oscar style.
167 Raw is a tiny place and you may have to wait a bit to get in, but laid back and casual lunch spot featuring seafood. Absolutely amazing.
Eater (online site) has a number of good articles about the “best” restaurants around Charleston that tend to be more on point than the recommendations from Yelp (at least as far as we have found).
It seems as though for every good restaurant we have...there are 2-3 tourist trap places. Hyman’s is a definite no-go. Gilligan’s is plain disgusting. You’ll see/hear lots of advertisements for these spots.
Enjoy your trip!
Chris
ETA: I recommend making reservations in advance for anywhere you want to go. The earlier the better. Prime times will disappear oftentimes weeks (and occasionally months) in advance.