Hi,
I am new to the forum too and spotted your question by chance.
I too was faced with the same dilemma earlier this year. I purchased an iPad Mini 64GB Cellular at the end of January and flew out to Greece for a 10 day holiday in early February. I flew to Athens but stayed in Nafplion, Peloponnese.
I tried to do my homework before leaving London for Athens but it seemed then that I would be in a similar situation to that which your Parents face now.
I found a similar thread to this one on the following website:-
http://forums.macrumors.com/showthread.php?t=924196
If, for some reason, the discussion does not load from this link then from the home page in the upper right hand corner there is a search bar and type in iPad Greece. The discussion is/ was about half way down the page.
I did telephone the then largest authorised Apple re-seller based in Athens and their website address is:-
https://foursquare.com/v/goldeni/4c9d99027c096dcb590fcdd1
At the time, most retailers had very limited stock of Nano SIMs and it was anyone's guess that they'd have any by the time I arrived. Owing to a public transport workers' strike in Athens on the day I arrived I had to forget about going to Athens for a SIM card and instead wait until I arrived in the Peloponnese.
Obviously, I feel I cannot help you further in your quest for Nano SIM providers in Athens but I did find that the Operator WIND in Argos was very helpful. They may have a branch in Athens?
WIND like COSMOTE and VODAFONE were more than happy to sell me a 'local' 3G Nano SIM for my iPad Mini. I made sure I took my iPad with me on the day. Their charge was quite reasonable, €14 for 1GB data.
What I hadn't banked on was that WIND would not sell me a SIM card without evidence of ID, like my Passport. Apparently, it is a national requirement that even Greeks have to provide ID when purchasing pay-as-you-go SIMs.
I left the shop empty-handed but safe in the knowledge that Nano SIMs for iPad Mini do exist.
I hope your Parents have better luck!
Best wishes,
Rob