The breakfast is great, the manages was very kind changing our room, as the air conditioning in our original work kept the room at 30ºC.....
There is no gym, which is a big minus, nor a swimming pool. A 4 star hotel should have them both.
The beach is private in some sense, but there are many rocks and difficult access to it. The pictures advertised on various web sites are misleading as they imply thet the shown beach belongs to the hotel, but it soes not. If you want to rent an umbrella and chair, you will likely pay 36 euros.
Overall nice place to sleep, and leave first thing in the morning after the great breakfast to explore the island.