Delos: a whole UNESCO island that is one open-air ruin
A 30-minute boat from the Old Port lands you on uninhabited Delos, an entire UNESCO World Heritage island that is one vast archaeological site -- the mythological birthplace of Apollo and the sacred heart of the ancient Cyclades. You walk the Terrace of the Lions, mosaic-floored merchant villas, the theatre and temples with the Aegean all around, led by a certified archaeologist on a wireless headset. This is the single regret-if-you-miss-it thing in Mykonos, and the ~10:00 departure returning ~13:30 fits a port window with margin.