I went there 3 times and completely fallen in love with that island.

The atmosphere is just perfect, alongside with water and landscape.

My favourites:
Beaches: Superparadise (snorkening), Ornos (food), Ftelia (to be alone)

Activities: Delos (archaeology, don't miss it!)

Restaurants: Avra for the dinner (very cute, with flowers and 100 years old cactus) and Hippie Fish for the sunset.

Place to stay: if you want to have a sea view, then something on the southern side. If you don't, try to find something in Klovas. It's cheaper, shops are nearby and you are on the main road so you can go anywhere.