Going to Santorini for 3 nights at the beginning of September. Want a place that is quiet, with private balcony to enjoy view. Trying to decide between Santorini Princess and Iliovasilema. Concern about Illiovasilema is the balcony/terrace (is it private) and the small pool area. Also Astra and Anastassis Apts are already booked. Any advice?