We had only one night in Bilbao, and this apartment in the Casco Viejo was perfect: 20min walk to the Guggenheim along the river, surrounded by bars and restaurants, and really comfortable for a couple. Josu even gave me access to his parking space for a great price and walked me to the apartment, providing great tips along the way.
One thing to note: the apartment is on one of the most popular streets in town, so you will hear the noise of bargoers, even though the windows keep out most of the sound. Secluded this is not! Didn't bother us at all as deep sleepers.