Mylopotas Beach [sometimes known as Milopotamos] is big and sheltered, with superb soft sand and plenty of good tavernas, alternative cafés, camp sites and discreet hotels nearby. Watersports facilities are also available. Milopotas is only just outside the main town, an easy stagger after a night partying.
Ios does have a bigger, better beach, Manganari, but it's 22km [14m] of hellish off road travel or a boat journey to get there, and facilities are either very posh or basic, though new road construction is underway and Manganari will really open up when it's finished. Currently Ios agencies run buses there from around 11am