Smart, upscale Skala is the island's main resort and anchor. The first thing you see as you enter town is the statue of Protergatis Xanthos Emmanuel, who became famous because he led an uprising against the Turks in 1821.
There a red buoy near the beach that is a reminder of the duel of miracles between the evil magician Yenoupas and St John. Yenoupas intended his miracle to be bringing back effigies of the dead from under the sea. St. John, however, prayed that Yenoupas be petrified while he was still submerged. This effectively ended the duel, but the petrified remains of Yenoupas under the harbor still stink of sulphur.
You can hike up to the site of the ancient city Kastelli in about 20 minutes. There are remains of a Hellenistic wall and the chapel of Ag. Konstantinos. The view is stunning, especially at sunset.
From Skala, you can see Chora above. A gem of Byzantine architecture, Chora clings to the walls of the monastery. It is walkable, but buses also make the trip. Chora has a wonderful panoramic view, a maze of alleyways, chapels, and lavish mansions. Many of the buildings have distinctive window moldings decorated with Byzantine crosses.
The Monastery of St John the Theologian (fee, modest dress required) is built behind walls that withstood every invader and marauder for centuries. Inside are narrow corridors, courtyards, chapels, tombs, and the Treasury Museum. The museum has many wonders including gold and silver crosses, superb icons, jeweled pendants from Catherine the Great and many rare manuscripts. Among the manuscripts is St Mark's gospel, written on purple vellum. (You have to get special permission to see it.) Orthodox Easter celebrations at the Monastery of St John bring hundreds of worshippers into Chora. The abbot of the monastery washes the feet of 12 monks to reenact the washing of the disciples feet before the last supper. The washing ceremony is on Maundy Thursday.
In addition to that prime attraction, there are 40 or so other churches in Chora. Especially worth seeing are the Convent of Zoodochos Pigi, Convent of the Evangelismos and the Monastery of the Apocalypse.
On the path between Skala and Chora is the Holy Cave of the Apocalypse. This is where St John saw the vision of fire and brimstone he recorded in the Book of Revelation. You can see the rock where he wrote and the indentation where he rested his head. There's a fissure in the roof, from which the voice of God was said to have come.