I began a tour in Bilbao about 4 years ago and I liked the town. For the OP, I went west from Bilbao. As MichaelW said, the Picos de Europa are great. There's a very nice road through a gorge in that region. Its number is AS-114 and it goes west to Cangas de Onis. The Mino/Minho valley along the northern border between Portugal & Spain, and then eastward entirely in Spain, was great, too.