Holy Mountain (Mount Athos) is an independent Republic of 21 large Monasteries thatgovern themselves in Greece. Women are not allowed at all to visit the sea-circled mountain, and even men need visas to do so. But monks are welcoming to those with visas, you travel with boat from Theassaloniki.
There are at least 8 hours of church services per day, the rest of the day is spent in labour. Monks only eat twice a day, and they eat very little, they never eat meat. So you should carry your own food with yourself, you are most likely not used to their fasting diet. You are of course free not to help monks in their labors or church services and you can wonder around, climb the Mountain, meditate in prayer, etc…
The mountain is the Garden of the Virgin Mary, the mother of God, and monks teach that it was Her wish that no woman puts her foot on that Mountain. The Mother of God is the official Bishop and Abbot of the Holy Mountain, and Patriarch of Constantinople serves as Her Vicar on the Holy Mountain.
If you go there, you will notice incredible silence and feeling of holiness in that place, it is a foretaste of Heaven.