HHI is definitely is a superb family vacation destination.
There are very good golf courses on and off the island.
The beach runs the entire length of island (12 miles). The beach is public and great for walking and biking. Most of the beach front consists of private homes with some commercial buildings. The Island has a three floor restriction. Certainly not Kiawah or Amelia or rural outer banks but not Miami Beach or Myrtle Beach either.
Biking is terrific. Besides having a seven mile uninterrupted stretch on the beach which is great for biking, the island has 60 miles of paved bike paths, is currently adding more pathways and is considered a Silver Level Bicycle Friendly Community.
As others have said there are a lot of great dining options.
Gregg Russell has outdoor concerts several nights a week at Harbor Town and is a great entertainer for young and old alike. Shelter Cove also has night time entertainers. There is a lot of entertainment for the family. This link offers plenty of suggestions.
http://www.hiltonheadisland.org/see-and-do/
In spite of having everything available on the island (restaurants, supermarkets, bookstores, Walmart, sports bars, movies miniature golf .....) the island's stringent building codes have helped keep the island from looking commercial. Most of the commercial properties are set back from the roads and have beautiful landscaping, creating the appearance that the island is less built up than it actually is. It does make it a little difficult to find things but worth the difficulty in my opinion.
HHI is a 50 minute ride to Savannah if there isn't enough to do on the island.
If you choose HHI, consider renting a condo or home. Plenty of good options.