I would recommend Naxos over Mykonos and with 12 days you could easily add Paros too. With Santorini, Paros, and Naxos you’ll get a good mix of different delights and some ferry island hopping too which is fun in itself. 1.5 days in Athens is perfect for most – 1 day for the Plaka, Parthenon, Acropolis Museum area; and a half-day to visit the Archaeological Museum which is a short drive or walk from the Plaka but hard to fit in one day along with the other sights.
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.
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