I'm also a local and there have been some excellent recommendations already made. Honestly, it's much harder to find a weak restaurant here than it is at WDW--most are good, many excellent. Here's my list to add to the confusion...
Fishcamp on Broad Creek: Excellent raw oyster bar, other seafood options also very good (one of the better shrimp and grits I've ever had), and solid wine list/drink menu. They DO take reservations either via phone or through Resy and have outdoor seating.
Ela's on the Water: A 10 to 12 minute walk across the bridge to Shelter Cover Marina. As someone else mentioned, it's a bit more upscale than most other restaurants but not stuffy. Quieter (it's smaller) but kids will feel very relaxed and welcome, too. They, too, take reservations and have outdoor seating.
Skull Creek Boathouse: One of the more popular restaurants on the island, and it can get crowded, especially on weekends, though as someone says, it's off season so shouldn't be too bad. However, they do NOT take reservations. Large outdoor seating area, great bar area (and has full menu), and plentiful seafood options.
Hudson's on the Dock: Another local joint, though I prefer Skull Creek Boathouse a bit more. Hudson's has great outdoor seating but only meh indoor seating area. They do NOT take reservations and can also get busy at lunch and dinner.
Hilton Head Social Bakery: Right over the bridge to Shelter Cove Marina next to Scott's Fish Market, it's a topnotch French patisserie serving sweets, quiche, sandwiches, coffee, breads, and more. It is pricey, very pricey (e.g., raspberry macaron is $8--granted it's palm-sized with fresh raspberries and a cream filling but still...).
Scott's Fish Market: I only mention this one because it's the closest restaurant to the resort (literally, a 4-5 minute walk), but it's only meh. Not bad by any means, but there are many better options to settle. Still, if you're tired, want hot food, and a decent menu selection, it's a solid option.
OMBRA Cucina: Best legitimate Italian on the island. It's a 5-minute drive and worth it. It is a bit upscale and often used for birthdays, anniversaries, etc., and while kids are most welcome, you'll find it more of an adult-oriented place with an extensive wine list. They take reservations; in fact, I'd recommend you make one.