This place was phenomenal. Note that it's actually a hotel called Villa Lukas. The hot tub was incredible for our stay in Mid September, the water wasn't too hot so we could lounge in there for hours and stay warm when the sunset got chilly. This is the best sunset I've ever watched in my life, and I don't know if anything else can ever compare - lounging in the hot tub watching the sun set with a completely unobstructed infinite view of the sea and horizon!
Obviously it's pricey but I have zero regrets picking this place. This particular room was also fairly private - on the Caldera you can often see into other people's pools and balconies but ours was one of the highest so we could see into others' but not many could see into ours. Being high up also means less stairs!
The receptionist Greg was phenomenal and helped us with our luggage for the stairs both at arrival and departure. They were also incredibly reliable with the transfers around the island and we scheduled both the airport pickup and ferry dropoff with them for 25 euros. We felt that Imerovigli was a great choice to stay at - Oia and Fira were too crowded for us.
Breakfast was served every morning right on the balcony and we felt so spoilt! The amenities were also excellent, we really appreciated the hotel slippers and bathrobes. On our last day they held our luggages so we were able to go off and explore in peace before our departure.
The only bad thing I can think of is that the shower doesn't have a curtain so the water tended to spray out. With that and the water trekked in from the hot tub, the already slippery floor tiles around the room were a bit of a hazard. Just ask for more floor mats and watch your step!