Look for sand dollars along the beach. A little bleach will turn them blinding white. See what kind of an artist you are. Grab a pencil or a pen and some paints and create your own masterpiece. Learn to throw a cast net.
Many local people use a cast net to catch mullet, shrimp and bait fish.
Visit the St. George Island State Park. Check out the county's lighthouses. The one on the island is in jeopardy, in part because the land around her is corroding away, so this might be one of your last opportunities. You can't go into it's tower, however, because the structure is also in serious disrepair. The Coast Guard has boarded up and locked the door, but the view is still breathtaking.