Mykonos had gay clubs and sunrise parties long before rave culture was even invented. Its bohemian allure hasn’t faded since the 1960s, although the once naked beaches now have nail bars, personal trainers and house music pumping out all hours. The influx of supermodels and superyachts has inspired hot new hotels and restaurants. The hippest place to show off your abs is Scorpios, a louche beach bar that puts Ibiza's finest in the shade (book a cabana to watch the sunset). After hours, it's always Astra, where you might find Keith Richards chatting up Karolina Kurkova. The gay crowd has dwindled, but drag queens and oiled bodybuilders make a splash at Jackie O, overlooking Super Paradise bay.
These groups are generally better connected among themselves than with other groups, so you are probably better advised to target them on this basis. As it’s your first time to Greece, you may want the full-on Greek island experience and you could easily fill your five weeks flitting from one island to the other in the Cyclades. You could start in Kea and work your way down to Milos via Kythnos, Serifos and Sifnos then segue to Paros and Naxos. Dip down to Santorini, up to Mykonos and back to Piraeus. The map will also show plenty of other Cyclades islands to pick and choose from such as Ios, Sikinos, Folegandros, Amorgos, Syros, Tinos and Andros – yes! too many choices, but you will find that sticking to one group it will be easier to get between them. Realistically for a period of five weeks you will not want to be doing more than 6-8 islands.
Yes, I would agree that 8 or 9 days is too long for Naxos – unless you’re happy sitting at the beach for several of those days. But if you’re looking to be semi-active and explore then you’d be best to add Paros and spend 4/5 days on each. Crete, on the other hand, would be perfect for an 8/9 day road trip. Start in Heraklion (where the ferry arrives from Santorini) head east and then south and finally ending up in the western town of Chania where you can fly up home from.
The Greek islands have beautiful weather in the months just before and after peak season. It’s a great time to see the islands, save money, avoid the crowds, and still have great weather (though not as hot as July and August). If you want to see the super-popular islands of Santorini, Rhodes, Corfu, and Crete without the tourists then this is a great time to visit.