There are no Oriental Orthodox monasteries on Mount Athos. I guess it is true to say that this is partly because Oriental Orthodox are not very welcome there. But it is mostly because the communities did not develop there until after 860 AD when the first small groups were formed. By that time the Oriental Orthodox were under the Muslim Yoke and there was a wide division between Eastern and Oriental Orthodox.
There are of course ancient monastic communities among the Syrian and Coptic Orthodox, many of which go back to the earliest monastic period. If you are able to accompany Abba Seraphim to Egypt then you will be able to visit some of these monasteries whose names will be well known to us all from the writings of the Desert Fathers.
The Desert Monasteries are our own Athos, much older, and over the last generation entering into a new and vibrant period of growth.
I can recommend the book:
Monks and Monasteries of the Egyptian Deserts.
<!-- m --><a class="postlink" href="http://www.amazon.co.uk/Monks-Monasteries-Egyptian-Deserts-Meinardus/dp/9774241886">http://www.amazon.co.uk/Monks-Monasteri ... 9774241886</a><!-- m -->
Which is a very interesting and readable description and history of the Egyptian monasteries.
Sorry, that plug is not about Athos.
But I believe that it would be hard for an Oriental Orthodox to visit Athos at the moment. And since there are so many Coptic and Syrian monasteries which would make you entirely welcome I am sure that you will find many wonderful places to visit if you have the opportunity.