There are a wide selection of villas, houses, apartments, and maisonettes available for rent in all the major towns and villages across Ikaria throughout the year. As Ikaria has not been heavily developed for tourism, it can take quite a lot of searching to find something which meets with your requirements.
Here are some links which should help speed up your search:
Vacation Rentals on Ikaria – HomeAway.
Ikaria Houses – Island Ikaria Online Guide.
Ikaria Accommodation – Ikaria Holidays.
Luxury Villas Ikaria – Luxury Vacations.
Accommodation in Ikaria – Paradizo.
Studios in Ikaria Island – Ikaria.gr