As someone who lives in Greece and travels often, I think Corfu, Sifnos, Kimolos, Crete, and Hydra are some of the best Greek islands to visit.
If you have even only a pebble-sized interest in Greece, then you'll have heard of the Cyclades, the stunning cluster of dusty emerald islands set atop the glittering sapphire of the Aegean Sea. But ...