I shouldn’t give this tip away, but you should see Folegandros, in the Cyclades. You definitely deserve at least a week on this ultimate greek island.
Stay at Provalma Studios and you’ll never forget such scenic view for the rest of your life, ask for Yannis your host, this guy will take great care of you. Have a dinner at Mimis in the gorgeous hamlet of Ano Meria -you cannot miss the grilled octopus!- Jump into blue waters at Agios Georgios after a panoramic ride on scooter. Hang around the Chora narrow lanes and find out your favorite taverna in the cozy squares. Toast with one or two shots of Rakomelo, a fine local honey liquor and you will be totally charmed by the magic of Folegandros.
Flying to Santorini from most European cities is way better than flying to Athens, because you can get to Folegandros in 40 minutes by ferry from Santorini. To check Ferries schedules Open Seas is great.