Hey, just came across your post. My family will also be in Hilton Head for Christmas! We're arriving the 24th and leaving the 27th.
We were thinking of bringing a whole turkey dinner with us (Super Target has a fully cooked special), then spend the day together as a family. With the events planned at the resort and the nature walks and the beach, I'm sure we won't be bored! We are definitely planning to take it easy, though. It's a very different vacation than the theme parks.
I was there a couple years ago for the holidays, and it's definitely the off-season for that area. I don't remember there being much to do on the island, even a lot of shops were closed that week. I would look at Charleston for something holiday-ish. A lot of the old houses are decorated beautifully for the holidays.
-Suzanne