See our greece hotels for a complete look at accommodations available on this island.
I will give you a tip as to where to stay if possible. Try to stay in town but out of the center because its noisy in town late at night due to the festivities. Also if approached upon disembarkation, to let a room make sure its not up in the isolated holiday apartments that has sprung up on the hills around the town.
Historically Mykonos was overshadowed by its close (30 min.) island neighbor Delos, which was, in its ancient heyday, the capital of the Aegean (or Cyclades anyway) and still well worth a visit today. In its most infamous period over 10,000 slaves could be sold in a day on Delos. Other days the inhabitants could be purified by the jealous Athenians and enslaved themselves. But (forgive me) what comes around, goes around, and today Delos is uninhabited.
If you look at an Aegean map you'll see that the Cyclades Islands roughly form a circle or Kyklos and from whence the name Cyclades arises. Since there is no letter 'C' in Greek it should be spelled Kyklades . . . but no one does.
The ancient Ionians first colonized the island of Mykonos and built three settlements of which little is to be seen. One is southwest of Mykonos Town (also referred to as Hora) on the isthmus near Korfos. Another, dating from 2000 BC is at Dimastos and the third at Panormos the big bay in the north, finally at Lino, near the airport are Hellenistic walls and a tower. Finds may be seen at the harbor side Archeological Museum in Mykonos Town (8:30-3, closed Mon, fee).
All 3 of these cities were destroyed by a war between foreigners: the occupying Romans and the invading Persians under Mithridates. The Roman Strabo noted that most of the male population of Mykonos was bald and bald men were laughingly referred to as Mykonians all over the Empire. Much later, under the Byzantines, Hora arose. Then came the Dukes of Naxos and later with the Venetian occupation, Hora gained a no longer visible defensive wall. At Old Castle or Paliokastro, Governor Ghizi built a fort which still exists. The Venetians ruled from 1207 to 1537 at which point Mykonos surrendered to the Turks and came to be a pirate island and was settled with pirate families who ran a very profitable business in pre-owned merchandise. However, they were very active in the 1821 War of Independence against the Turks and contributed 22 ships led, once again, by lady Admiral (as on Hydra) and national heroine, Manto Mavrogenous whose bust is in the main square.