If is a very special experience if you can dine with the monks in the official refectory of the monastery. But not every monastery allows non-orthodox visitors to join them. Sometimes you will arrive at an inconvenient time
so dining in the old refectories is not possible then. Your place as a non-orthodox in church is also dependng on the monastery you visit. In most cases you are allowed to stand in the back of the church, the narhtex. For me that is good enough because there is still a lot to sea and hear. Here is information about the customs at some monasteries.
Vatopediou – non-Orthodox pilgrims must remain in the narthex during services, but may eat together at a table with Orthodox pilgrims
Xeropotamou – non-Orthodox pilgrims are forbidden from attending services but may view the church at other times in the company of a monk, and can eat only after the monks and Orthodox pilgrims have finished dining
Simonopetra – non-Orthodox pilgrims may sit in the main sanctuary during services
Esfigmenou – non-Orthodox pilgrims are forbidden from entering the church, and dine at the same time as monks and Orthodox pilgrims but at a separate table
Hilandariou – non-Orthodox pilgrims must remain in the narthex during services, but may eat together at a table with Orthodox pilgrims.
This is information of the situation in 2006.
Lavra – The two times I (hv) visited this monastery I dined with the monks in the old refectory and stood in the narthex. See picture taken in 2007.
Pavlou – I stayed two times here, the last time in 2007. Diner was always in a small kitchen near the pilgrim sleeping quarters. See picture 2007. But in 2011 we ate in the refectory separate from the Orthodox but also separated from 2 catholics!
Stavronikita – we were able to eat in the refectory together with monks: a German Greek speaking non-orthodox pilgrim of 80 years old was allowed to join the service in front of the church, we were placed in de narthex (2007).
Konstamonitou – In 1997 I was not allowed to eat together with the monks, and we could not visit the katholicon during a service.
Dionysiou – 1986: easter-service in the narthex, food together with the monks in the refectory.