The Mirador de Selkirk is a steep saddle high above San Juan Bautista where Alexander Selkirk used to climb to scan the sea for passing ships. The walk takes about three hours up from the village through native forest of myrtles and tree ferns, and the path is rough but well marked. At the top you stand on a knife-edge ridge with the inhabited east coast on one side and the wild west coast on the other.
The view is the whole point. On a clear day you can see right across to the empty western half of the island, with the South Pacific stretching unbroken to the horizon. Bring water, a windproof layer, and reasonable knees.