We had a wonderful time at the Karpimo Suites, Aspa House. The apartment has a smart layout and is nicely decorated. There's shared outside seating and a small pool. The host is very friendly, speaks English fluently and gave us really excellent tips for sightseeing and restaurants across the island.
The complex is situated on the quieter east side of the island. Less than 10 min from the airport and close to the beaches. All the other famous locations are just 20-30 min away with a rental car (or quad bike)
Highly recommended if you want to visit Santorini and don't want to stay in the crowded tourist places, like Oia and Fira.