Your visit to Mykonos must be combined with a visit and tour to nearby Delos. You can reach the "sacred island" by sea while there is no other connectivity but from Mykonos.
You can take one of the boats departing from Gialos and find yourself in one of the most important archaeological sites in the world within 30' tops. There are daily itineraries, at specific times every day and the return ticket costs €19 per person.
From the moment you arrive at the archaeological site, you will be charmed by the light and energy of the landscape. Some of the main attractions here include the house of Dionysus, the Lion Terrace, the Sacred Lake, the Agora of the Italians, the Temple of Delians, the Temple of Hera, etc.