I recommend the Gran Hotel Don Pelayo in Covadonga, right next to the magnificent Basilica of Covadonga. A 4-star hotel, very comfortable and spacious. In midsummer the temperature is 20º. The food is very good and the views are unparalleled. Approx. € 110 per night.
The Bricial is one of the charming hotels of La Pasera group that lies between Cangas de Onis and Covadonga. The rooms are well equipped, and there is a good restaurant which offers breakfast and lunch. They offer deals throughout the year including Sella river descents, quads, Cares route, Jurassic Museum entrances. I recommend reading the web to keep up to date with the special deals. A weekend deal costs 100 € (2 nights).
The truth is that it is one of the places I've been to repeatedly when making a trip to Asturias. Besides having the luck of being located in Cangas de Onis, is is perfect value for money. Simple, clean, good people, better food ... There are a few places to stay: The Pasera, The Bricial, and La Trappe Angliru Palace. The latter is my favorite and is the one in the photo. 100% recommended