Are you dedicated to staying in Athens? Or are you just figuring that no one will be willing to pay for you to come to the US/UK/whereever. Because if it's the latter, I think you would be surprised.
You need to concentrate on just getting a foot in the door, and worry about how to leverage that into your ideal career once you've got that worked out.
(And just let me clear, I'm not saying only apply to larger companies. I'm saying, play the whole field for now.)
can give a list of few of the prominent companies that could do offer 5-6months internship & cover living costs.