According to this sketch, taken from the Zwerger-map (sept. 2001), the postoffice (TTT) can be found near the Protaton church and between the embassies of Karakalou and Xenofontos (numbers 10 and 13).
The centre of Karyes – Athos map from Reinhold Zwerger- A-1020 Wien, Wohlmutstr. 8
If I remember correctly that there were some more houses in this area of Karyes a couple of years ago and I don’t know if this city plan is acurate and up-to-date. The postoffice should be on the right side of this picture near the white building ?
This letter shows some rare examples of Mount Athos stamps from 1916.