Hi, there are no pilgrim albergues near the cathedral, only backpackers’ hostels, of varying quality. I’ve tried a few, just because they are cheap, but wouldn’t recommend any of the ones I stayed in. For a quiet night you are better off in a pension, if you want to be near the cathedral. I now always stay at the Gallery Hostel
http://www.gallery-hostel.com/en/ which is nowhere near the cathedral, but which I can
highly recommend, and no need to book one of their private rooms either, as the dorms are great.