Public transportation in Athens and in Thessaloniki is not free of charge for refugees. There has not been any directive from the government to guarantee free transportation to refugees.
People have to pay for a travel pass or ticket in order to use public transportation. If you do not have a valid ticket, you may be fined.
In Athens, a so-called integrated ticket, valid 90 minutes in buses and in the metro, that would take someone for example from the port to the city, costs 1.40 euros or 60 cents, if discounted for kids aged 7 to 12 years, families with more than three children or people older than 65.
A similar trip in Thessaloniki would cost 1 euro or 50 cents discounted.
Failure to display a valid ticket or travelcard may result in a fine which is 60 times the price of the ticket, both in Athens and in Thessaloniki.
For example, in Athens, a fine would be 84 EUR for those who are obliged to use regular ticket and 36 EUR for those travelling on a discounted ticket.
For more information:
Tickets and travel cards in Athens: http://www.oasa.gr/pdf/en/TICKETS_AND_TRAVEL_CARDS.pdf
Fare Controls in Athens: http://www.oasa.gr/content.php?id=elkom&lang=en
Fare Controls in Thessaloniki: http://oasth.gr/#en/fare-inspection/