Deportivo Alaves is solid, typical province club with a familial character. Even though they reached in 2001 the historical final of the UEFA Cup (5-4 loss against Liverpool), historically they are a modest Spanish club. The club is very accessible for fans: the training ground Ciudad Deportiva José Luis Compañón (Ibaia), a little west of the town is regularly open for the fans.
Bonus tip: The old training complex van Alavés, the Complejo Deportivo de Betoño, is also worth a visit. It's currently used by a lot of local teams and has old and small stand.