We have a home on Hilton Head, so I spend lots of time there! Where will you be staying? Most plantations are restricted access--which means that you will pay a gate fee (Sea Pines) or have a reservation (Hilton Head Plantation) to be allowed in.
For adults, there are several favorites, each of which serves wonderful food. Red Fish on Palmetto Bay Road has great food, a lovely dining room but does not offer wonderful views. It's right on the road. Still well worth it. Tapas offers even less in the way of atmosphere, but the food is wonderful. Probably the restaurant that offers both atmosphere and good food would be Old Fort Pub in Hilton Head Plantation. Bear in mind that Hilton Head is very much a family destination so you would not be assured a child free atmosphere anywhere you go.
For kids, there are lots of choices. The Crazy Crab in Harbortown doesn't have stellar food, but is a fun place. It's almost a must do, but do it late enough that you are there for Greg Russell's concert (at 8, I think, during season). He's a hoot, both for kids and for adults. (Think "yuppidy do dah" when hearing kids names today and a song called "Is that a booger in your sugar, not it'snot.) The Salty Dog Cafe is just about 3 minutes from our house, and they too have children's activities and live music during season. You have a choice there, either eat from their "cookout" on the dock area of the marina, or eat inside at Captain John Braddocks. The Salty Dog is the personification of what Hilton Head is, at least for us. I know that I'm there once I sit and look at the boats while drinking a frozen Pina Colada. For breakfast, there are a number of choices...IHOP, Original House of Pancakes, Hilton Head Diner, Stacks and the Sunrise Cafe at Palmetto Bay Marina. Oh, and Marley's is another good dinner spot with live music that kids seem to like.
If you want to see dolphins, there are Dolphin cruises or, if you want close and free, go to Palmetto Bay Marina in the afternoon (I think around 3) and wait for the shrimp boat to come in. I tried for close to 15 years for a dolphin shot (had it pictured in my head), took lots of the dolphin cruises, and finally got it and many more one afternoon at Palmetto Bay marina.
And of course, there are the beaches, the bike paths, miniature golf, horseback riding, shopping and time to just relax. Just got back to Maryland a couple of weeks ago, and think I'm here till April. I'm missing the alligator who hangs out in the lagoon behind our house! Which leads to a PSA--do NOT feed any alligators. It's against the law, and is really not good for them. They are intelligent enough to realize that food comes from people, but not intelligent enough to realize that people are not food. Once they become aggressive, they are removed and killed. And I've seen one guy in our lagoon haul himself out of the lagoon and directly at some very surprised folks on the other side of the lagoon from me. Alligators can run faster than a man, so these folks were lucky...even though they had been feeding him that morning.