Last time I was in that area was about 7 years ago. Every time I've been I've had a car and been touring.
Great eating, drinking and very picturesque.
The Picos are a sight to behold. The trip to the Fuente Dey cable car and that journey up the mountain is awesome. Might be too far away as might the Rioja region.
Lots of quaint wee villages, some walled villages Santillana del Mar probably the pick of the bunch.
If you don't have accommodation register with the Paradors http://www.parador.es/en. Stunning hotels run by, or at least used to be, by the Spanish Government and held as a standard for others to aspire to. You can get some really good deals.