Founded in 962, the working Byzantine Monastery of St George (whose bells might wake you early if you're staying in town) crowns Skyros Town, within the lower walls of the Byzantine-Venetian fortress. You can visit its 17th-century chapel, which features an ornate gilded screen and faded 18th-century frescoes.
Follow 'Kastro' signs through the twisting whitewashed lanes of old Skyros Town to get here.