We ended up staying at Stelios Pension and our stay was amazing! The owner was kind and helpful every time; if you need something it's easier to reach him with a text and he promptly replies.
He picked us up from the airport and immediately showed us around and gave us the basic informations to go around the island. The property is well located and close to it you'll find an atv/car rental, a post office and a mini market. Mykonos downtown is literally few steps from it.
The room was nice, furnished with basic furniture but comfortable.