This is probably one of the best Airbnbs I have ever stayed in. Imerovigli is a small town along the road between Fira and Oia. It's much quieter and calmer than either city, a great spot for relaxing.
The airbnb is located deep down the caldera away from the foot traffic of the road between Fira and Oia. The patio is fully private, and it's large. You'll notice compared to the other two spots, this patio is the best. The room comes with great amenities, coffee, tea, sugar, fridge, A/C.
Nikos and his team are fantastic, they great you hospitably. Explain the town to you, explain the sites, and Nikos is so responsive. This is truly a well oiled business.
I rarely want to re-visit a destination, but I can tell you I would be back to Santorini and I might even stay here again.