No worries...
I think the activities vary based upon the weather, and they do have Winter, but you can still have very nice weather there in January. If it is one of their milder times, you will be able to do a lot outdoors...bicycles (on the beach or on the many paths on the island), shuffleboard, ping-pong, etc. Fishing for crabs off of the pier is fun, especially for kids, although I THINK they do better in warmer weather. They will do some craft activities and games and stuff indoors. Hilton Head is a very developed area...although done in a non-invasive way. Miniature golf courses there are fun, I think you get a coupon for one with your check-in materials. If you hit a crummy day there are movie theatres very close.
If you're interested in eating out there are a ton of options for families, plus I think Hilton Head has always had a kids night out which allows the adults to grab a quiet dinner on their own. Some restaurants are closed that month, but I know there is always stuff in Harbour town (which has a great playground.) Crazy Crab is one of our favorites down there, but we actually prefer the one as you enter the island which has a huge fishtank and a great Marsh view.
