Ignacio,
How about the Plaza de Artxanda? The Funicular de Artxanda would also offer a nice opportunity for him to rise above the city and look at it from Mt. Artxanda. Great restaurants in the area and a few grills if I remember correctly.
They also serve tapas there too I remember.
I enjoyed stepping out on the balcony of the apartment we stay in when we're there for extended periods of time, and looking up at the mountain and the lights as they come on in the evening at dusk. It's a great sight.
Now you're making me hungry, and I want to get back to Bilbao and visit my friends...
Wolf