We LOVE going to Hilton Head! My kids' favorite place in The Frozen Moo in Coligny Plaza. They have enough flavors to make your head spin. There are many places that you can rent bicycles from that are pretty reasonable. You can typically get to the beach, restaurants and shopping via bike instead of car from many resorts. HHI is very flat, so it is usually a very easy ride. The beaches are hard-packed, so you can ride on the beach, too. Check with the resort you are staying at to see if they have an arrangement with any of the bike rental places to get an even better deal. The one we have used several times is
Hilton Head Island, South Carolina Bike Rentals - Rental reservations ONLINE. Get the baskets, you will definitely use them.
We have found many great restaurants, but one of our favorites is Sea Shack, which is off the beaten path and always a wait for a seat, but soooo worth it. We have gone there every time we have been. This is not fine dining (dinners are served with all disposable items), but is one of those "locals only" places that is awesome. We also like Steamers in Coligny Plaza and The Smokehouse.
Have a great time!!!