My father and I stayed in one of Vasilis's cave houses for four nights (pano meria 3). It was a wonderful! Bigger and better than the photographs and squeaky clean. There are quaint features such as little alcoves and exposed rock and plenty of storage.
As for the view, it's to die for. So long as you've respectful neighbours you can sit on the balcony and enjoy the silence while looking to sea for hours, away from the hustle of the main streets though they're only 2 mins away! I'd recommend these apartments to anyone visiting Santorini. Such good value as the hotels are extortionate.