More than a correct place is the Hotel Mieres del Camino, very nice for its good atmosphere, ideal to rest and relax in their rooms designed for it. The quality-cost relationship is the best you can find in Asturias, and specially if you deal with the staff, very attentive to customer service to get your comfort.
Something simpler to sleep in Mieres is to choose the Hostal Pachín, clean and correct in its facilities. It is very well located if you want a simple option located a step away from the majority of the attractions of the town. If you want to enjoy the town at a good price, this is an ideal place.
For the pilgrim community there is the Pilgrim Hostel of La Peña, where the recepcionist will be the best people you will meet during your experience, at the service of their clients to facilitate anything. It is a fairly cheap place to sleep in Mieres.