To avoid
Don't forget about the region's heritage, one the Greeks are very attached to; it offers a great way to mix in with Greek holidaymakers. Try to speak a little bit of Greek if you can, as English is not the official language here even if most of the people working in the tourist sector can speak it. 'Kalisto' and 'efralisto' are two essential words (hello and thank you).
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To try
The Greeks enjoy fine gourmet cuisine, and the mix of more refined Mediterranean flavours in particular is a real culinary delight. Instead of limiting yourself to the traditional Moussaka, you should definitely have a taste of some of the less-pronounceable dishes - you won't be disappointed!
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To bring back
You can't go to Greece without bringing back some virgin olive oil! You'll have no problem finding the farms where it is sold, as they really are everywhere. Another speciality is the "sweet spoon", which is available in many different flavours: olive, melon, lemon, orange. A sweet spoon is a kind of bitter jam that can be enjoyed both before and after dinner. With Greek beekeepers holding the secret to creating thousands of varieties, honey is another of Greece's delicacies. Finally, those who love a good wine will be very interested to know that this region is home to large expanses of vineyards, constituting the perfect opportunity to bring back a good bottle or two.