As
muppets3d said, there are close to 300 restaurants in the area, and most of them are quite good to excellent. You pretty much can't go wrong unlike at the World. Plus, everyone will have their favorites, so it's tough to choose just a few. . .but I'm gonna anyway! I lived on HHI for two years (and worked at the resort), and a few places almost always worked for me. To wit:
Local flavors/ingredients
1.
Hudson's on the Docks: It's a true local favorite, and they try to use fresh catches whenever possible on the menu. Pretty darn good hushpuppies, too. They do NOT take reservations, but if you get there early enough before dinner or lunch, usually there's no problem getting a table. If weather allows, ask to be seated outside on the water.
2.
Skull Creek Boathouse (not to be confused with Skull Creek Dockside): Another local favorite, and they do NOT take reservations, either. Their Seafood Throwdowns are among the best, if not the best, on the island. Huge menu with tons of choices to satisfy pretty much everyone's palate. Again, go early or prepare to wait.
3.
Fishcamp on Broad Creek: Very good raw bar and excellent drinks. Menu is more limited but still good. They DO take reservations.
Fancier (for the record, few places are totally upscale where you wouldn't feel comfortable in nice jeans and shirt)
1.
Nunzio: Excellent Italian-based dishes, many with locally caught, fresh seafood. Exceptional service and wine menu. They DO take reservations.
2.
OMBRA Cucina Italiana: They DO take reservations, and is one of the more upscale places to dine on the island, though there's no listed dress code for it. Great service, excellent food, and intimate.
BBQ is a big deal in the low country, but I'm not a huge fan given it's so heavy and filling. So, I won't make any recommendations for that style of local flavors. I'm sure others will have plenty to say about that category. Enjoy!
P.S. Tide Me Over on the resort has Mickey waffles, usually made to order, and Dole Whips (including adult versions), so that should give you some good vibes.