South Point on the Big Island is the most southern point in the United States. The cliffs were ancient mooring places for canoes belonging to the first settlers on the Big Island. Fishermen still use this place to cast their lines, and adventurous locals dive into the turbulent but clear waters below (not recommended for tourists who are not aware of ocean currents, as the undertow is usually quite strong and has swept many lives away in the turquoise clear waters).
Several miles up the beach (toward the Hilo side of the Island) is the Green Sand Beach colored by olivine that formed as part of the volcanic eruptions long ago. It is worth hiking to (or paying for a local to drive you in their 4x4). Green Sand Beach is one of only four green beaches in the world.