Hilton Head lacks one of the South's best travel sites: old buildings. Luckily, Bluffton (roughly 12 miles out of HHI) makes up for what HH lacks.
This particular church was built in the 1800's and is still used today for worship. It's a beautiful building with a remarkable view of the water right below. You can even walk down to the dock to launch of boats or kayaks and dolphins are often seen in the area. If you're there to just see the building, it's best to avoid Saturday afternoons and all of Sunday.
If Bluffton doesn't satisfy your thirst for old buildings, travel down a little further to stop by Savannah, GA where practically every building is still in tact from the 1800's.