Keep the food recs coming in!! Headed there in a few weeks and furiously writing down all your suggestions!!
Fresh seafood to cook on your own
Bennie Hudson's Seafood Market (12-15 minute drive)
Barnacle Bill's Fresh Seafood (5-7 minute drive)
Kroger's in the Shelter Cove Towne Centre (2-3 minute drive; 10-12 minute walk)
Seafood restaurants
Scott's Fish Market (2-3 minute walk across the bridge): solid food, decent service, but location makes it a player
Ela's on the Water (5-7 minute walk across the bridge): excellent food, good service, and better at social distancing
Fishcamp on Broad Creek (12-15 minute drive): excellent food, excellent service, very good at social distancing
Skull Creek Boathouse (12-15 minute drive): great atmosphere, superb menu, but doesn't take reservations, always busy
Hudson's Seafood House (close to Skull Creek Boathouse): a popular local joint, we've had great food and service and meh food and service. Still, worth a look.
The Black Marlin (15 minute drive): solid food, good social distancing, good service
Others will undoubtedly suggest other worthy places, but these are our most frequented spots.
Other restaurants
Word of note here: we don't do pizza or BBQ or burgers or Tex-Mex while on the island--we get plenty of that where we live if needed. We prefer to go for seafood.
OMBRA Cucina (5 minute drive): Topnotch Italian; annually one of the top-rated restaurants and chef-owner in HHI
Michael Anthony's Cucina Italiana (8-10 minute drive): rivals OMBRA in most aspects; they do great curbside delivery, too
Hilton Head Social Bakery (sits beside Scott's): great pastries, quiches, etc. Only open from 8-4, but great for late morning or mid-afternoon brunch items, or take back to room for later. Expensive but good.