Folly Field would be the closest public beach to the airport. Bonus, it faces more or less east so you can see some nice sunrises.
Here is a map from the airport to Folly Field. To get to either one, do NOT take the Cross Island Expressway after you are on island, stay on 278. Eventually you will see signs for the airport - it's pretty small FYI. Folly Field is further up 278, and it's a left hand turn - on the corner is a Carabbas so keep a lookout for that.
http://maps.google.com/maps?hl=en&q...ljp1323311848499030&um=1&ie=UTF-8&sa=N&tab=wl
FYI my ride in the B-17 bomber was at Hilton Head's little airport.
http://www.flickr.com/photos/skywalkerbeth/5599942987/
You'll note that HII is shaped like a sneaker. Harbor Town in Sea Pines is along the instep, heading to the toe. That's a pleasant place to walk around. You can take boat rides from there too. I saw a whole mess of dolphins playing in the water a few weeks ago.
One place I visit on each trip is the Skull Creek Boathouse. It's off Squire Pope Road, which is the first left turn after you are finally across the bridge and on Hilton Head Island. Here is a photo of its pier, taken from the bridge near sunrise:
http://www.flickr.com/photos/skywalkerbeth/2914886493/in/set-72157604068550802
Turn left on Squire Pope Road and shortly after the roundabout (which is a ways down the road) you will see a sign on the left for the Boathouse. The food is decent, not fantastic but decent, but, it's such a pleasant place to sit and watch the boats and the water and the sunset, drink in hand. They have a lineup of Adirondack chairs facing the water/boats etc. If the weather is nice: 100 yards up the road, if that, is an outfitter for kayaking.
Anyway, about the adirondack chairs/drinks: my photo below (embedded) is me a few weeks ago. That's a Fat Tire, they have it on tap there.
Another thing to consider: Route 46, which is the road you'll be on when you turn into the Inn (well, again, it's three different numbers for the same road, at some point it becomes 46), is one of the "famous" canopy roads in South Carolina.
See this link, and in fact this would be a pretty drive. Explore to find these roads. Although I am not sure if December would be quite the same. They should stay green, IIRC. They are live oaks.
http://npaper-wehaa.com/bluffton-today/2009/11/19/#?article=656435
Note this statement from the link:
That is where you will be. Keep on it, and old town Bluffton is cute (very small). Lots of little art galleries. Plus there is an adorable little church right on the May River. Here it is:
http://www.flickr.com/photos/skywalkerbeth/2914883947/in/set-72157604068550802/
There are a few little restaurants across the street from old town Bluffton. Corks is a nice wine bar. When you hit Calhoun Street, roughly, instead of turning into the older looking part of Bluffton, instead turn the other way into an area that looks newly built. Corks is back there as well as another restaurant with a huge outdoor covered patio.
If you feel like it, Sea Turtle Cinemas, which is off Buckwalter Parkway, has movies. In that same plaza is Paulie's pizza (woodfired) and don't scoff, it's in my top 5 of favorite pizzas anywhere. And I've had pizzas! They also have outstanding chicken wings (baked not fried - and huge).
ps. And Beaufort is definitely worth the drive. It's not far at all, from the Inn I would expect maybe 45 minutes? Again it's going to take you ten minutes just to get off the Inn property. I have a little book which I bought in Beaufort which details the various movies made in the Low Country around Beaufort (probably Savannah too, although I can't remember for sure).
Another thing I just remembered: there is a movie-tour of films made in Savannah. That looks like fun.
Here's another tip: Savannah has a fairly active facebook page for visitor information, as well as the Savannah Film Office, etc. Do some facebook searching (or just click info on my page, open up my "likes" and then do a simple search on Savannah and Hilton Head. I've liked many pages.)
Here is one to check out:
https://www.facebook.com/SavannahHollyDays
or
http://www.savannahhollydays.com/