Follow that and you’ll soon arrive to the main shaded pathway leading to the monastery. Though the sign for the monastery points left, its entrance is actually on the right. No matter, left will take you where you need to go in order to reach above the monastery and enjoy amazing views over the island before starting the “real” journey.
You will want to look down towards the right until you find the monastery’s wall at the bottom of the slope. This is where you should aim to arrive. Once you get there, you’ll see a sign which (mistakenly) reads Mt. Eros. You should see two trails before you, one running parallel to the stone wall, and the other continuing away from it. This is the one you need to take. It becomes more defined as you continue on through the trees. The path heads slightly upwards for about fifteen minutes before curving towards the left. If you look to your right, you should see another clear path. This is the one you want. After a few minutes, your view opens up to the sea before you. From here you can continue down the zig zag trail, but it does not lead to a beach, rather, to goat farms and after several hours, the convent of St. Nicholas.
Most likely, you’ll prefer to simply hike the trail back in reverse before arriving back into the edge of town. From the church of St. Constantine, follow the steps on the side of the church, and eventually make your way down to the harbor.