We go to HH often, so I have to plunge in here. We don't care for the Old Oyster Factory or Hudson's (except for Hudson's in the winter months when they are one of the few restaurants that pull oysters out of the creek and serve them fresh). Our favorite traditional fried seafood favorite is the Crazy Crab as you come on the island (not the one in Sea Pines). The fried seafood is very good, and their hush puppies are the best (slightly sweet and peppery). It has beautiful marsh views and is very good place with children. There is a fenced-in playground beneath an outdoor deck area where parents can sip their wine while waiting for a table and keep an eye on the children below them. For a reasonably priced meal in a place where you will be comfortable with children, Captain's Seafood (on the highway to the right of the villas).
For fine dining, we like Le Bistro in Pineland Mall. It's small and stays pretty crowded, but the food is outstanding. Charley's on New Orleans Road is also good, roomier with a nice atmosphere. Old Fort Pub is good for a romantic evening, but I don't know that I'd take children there - pretty expensive. Fratello's is very good Italian across the highway and to the right of the villas, in one of those strip malls. Definitely should make a reservation for any of these places.
We used to go to San Miguels, but discovered a very good Mexican place down toward the bridge. I wish I could tell you the name of it, but it's located on the right as you come on the island, right before you get to the toll road exits. There are a few buildings there on the right - I think they have a sign for the Mexican place. We still go to San Miguels for outdoor drinks and the music.