8-9 days in Asturias

I am helping a couple in their mid 20s plan this part of their summer trip to Spain. They will not have a rental car. They would like to spend a few days on the coast, a few days in Oviedo, and a few days in a mountain pueblo.

I thought that either Luarca or Cudillero would be good for the beach part. At least Cudillero is near a couple of pretty amazing beaches (Playa del Silencio, Playa del Aguilar), both of which would be about a 5 euro cab fare from Cudillero. I haven't found similar beaches close to Luarca, but I imagine there are local beaches nearby that are pretty. Luarca is larger, so that might be a factor, but those beaches near Cudillero look lovely.

For the mountain part, the obvious direction to go is east rather than west of Oviedo. Maybe a few days in Cangas de Onis, but I'm concerned that without a car they won't see much of the Picos. And if they go east to Cangas, it would make sense to move the coastal town over to the east of Oviedo as well. That would suggest San Vicente de la Barquera, Llanes, Lastre or Ribadesella as a town from which to explore beaches. But I don't know much about the beaches in that area.

So, my main questions are -- should they drop the mountain idea because of the limitations of public transportation? If no, is Cangas de Onis the best choice? And any ideas on the coastal town?

Many thanks.