As noted by everybody else, the staff is amazing. You get the impression that they are taking personal responsibility for the quality of your overall stay on the island--not just that Afroessa itself is to your liking. Some things to point out.
They are very responsive beforehand via email if and as you try to figure out which room to book. As with other neighboring properties, Afroessa is not a standalone building but rather a collection of rooms built across varying stories along the caldera (cliff). Some have more privacy, others less. Some have more flights of steps to get to, others less. Etc. etc. They will help you decide (based on availability, of course).
While there, they welcome you as family and that's not just applicable to the owner. Eddie is "the man" -- he has gotten shout-outs here before but he really is always there to help with any request and the guy is a beast in terms of helping with luggage. Any tips you need or help booking reservations, the staff has got you covered.
As others have noted, the property is amazing. Fantastic air conditioning and very comfortable shower. We didn't have dinner there, but the lunch (same menu, I think) was excellent if you're looking to stay in. The pool gets fantastic late-afternoon sunlight.
The location is good for those willing to get some exercise while walking to and from Fira. The location of the hotel (Imerovigli) is ~1.5 miles from Fira but that is no ordinary 1.5 miles. It takes about 40 mins and especially on the return (since it is more uphill -- Imerovigli higher up than the other neighboring towns) is quite the work-out. We loved it bc before/after dinner + drinks in Fira, we were forced to take a nice long walk along the caldera path and you get to see all of the different hotels/restos/shops along the caldera. Parking is a <5 minute walk from the hotel (you make your own spot where feasible in one of the little alleyways or squares).
On the rooms: Rooms count up from the top down (room 1 is the highest up at road level). Rooms 11/12 are the furthest down the cliff (about 5 or 6 stories). The path along the caldera is about 2 stories down from road level. The further down, the less traffic you have passing by since there are fewer rooms to get to. As a result, they have the most privacy.
Cannot recommend this place enough -- awesome!