Monastery of St.John
The monastery of St. John is a thousand year old edifice which includes a museum which displays ancient artifacts, treasures and typographies and a gigantic byzantine church. The best time to visit the monastery of St. John is in the morning as it allows you to boycott the crowd and heat thus letting you enjoy the excellent views from the monastery. Ensure you inhale the peaceful and tranquil atmosphere around the monastery before departing.
Cave of Apocalypse
Irrespective of your religious affiliation, you should definitely see this important cultural site in Patmos. It is also a UNESCO World Heritage site. The church built southwards of the cave offers tours on which you can learn all about St. John of Patmos and his revelations in 95AD through a cleft in the rock. You can purchase an English copy of the Revelation in tourist shops to prepare yourself for the experience further.