I've been to Hilton Head Island in Feb. and in April many, many times. It should be super quiet at this time of year...many of the seasonal things are not open-like Salty Dog Cafe-the year I went for Presidents week in Feb. it was just opening for the season later that week. Their indoor restaurants and shops are probably open at South Beach Marina though.
Rent bikes-go for bike rides on the beach. The sand gets really hard packed at low tide so it's easy to ride your bike. Ride bikes to Coligny Circle and go the the little bakery for a treat.
Go down to Harbor Town and go in the lighthouse and the shops.
Do you like to golf or play tennis? There is plenty of opportunity for that on Hilton Head Island. There are also a couple of great mini-golf places-I'm not sure if they are open this time of year though.
I doubt it would be warm enough to go swimming in the pool or at the beach.
There are really good restaurants. Some of our favorites: Old Fort Pub, Charley's Crab, CQ's.
There is the Coastal Discovery Museum too. I've read of a children's museum-but I've never been there.
Savannah, GA is a short drive under 1 hour for a little excursion-well worth the trip-very neat place!
Have a nice trip!