Right, let’s get this out of the way first: the best Greek Island for partying is Mykonos. The narrow streets between the white cubist houses are full of people, from a distance all young, all beautiful and all impossibly fashionable. But that too is a trick of the light. When you look closely, you realise they are just the same people you stand next to every morning on the Tube, miraculously transformed for a fortnight a year. And they probably think the same about you. mykonos.gr
Farmakonisi was where Julius Caesar was held as a youth when kidnapped by pirates. He wasn’t impressed, so when he became general, he crucified the entire population. They haven’t really recovered yet. As such Farmakonisi remains uninhabited. You can hitch a lift with a passing yacht on nearby Arki or Gaidaros - just remember to bring your own grub.
The undiscovered gem of the islands, until now at least, is Gavdos. The southernmost island in Europe is what most Greek islands were like 40 years ago, and joy of joys, you are welcome to sleep on the beach. A local population of fewer than 40 with the necessary, small but growing number of artists and drop outs from the rest of Europe = Boho heaven! gavdos-online.com