Do hotels and apartments in San Stefanos generally have room safes? These are now very common in the UK and Italy, but haven't been to anywhere in Greece for some years, so this may be a stupid question to ask!
As a general rule, most places do not have a safety box in the room itself, but many are now upgrading to that, as above mentioned.
Thomas Bay Hotel and Athina Hotel have boxes in the lobby area, both travel agencies mentioned supply free boxes, (as they hope to change your currency there), San Stefanos is pretty much crime free anyway, but use a box for peace of mind, Passports etc are difficult to replace.