There are lots of apartments and villas in the area.
We recommend staying around the cove of Porto Rafti:
Some examples:
PORTO BLUE LUXURY APARTMENT
https://www.booking.com/Share-rgjhs4
Alme Sélas in Port Rafti
https://www.booking.com/Share-2ii3Ij0
Apartments MARE BLU by the sea.
https://www.booking.com/Share-YHiUu7
If you're feeling adventurous:
Camping Tents with Garden Hanging Bed