Nightlife in Vitoria is concentrated in the old town — particularly Calle Cuchillería, the so-called "Cuchi", which runs the length of the upper medieval quarter and stays loud until two or three on weekend nights. Below in the Ensanche, the bars are more polished and the crowd is older.
The Basque pintxo bar doubles as a drinking bar, so the same places you ate at earlier in the evening are where you finish. For later cocktail and live music venues, look around Plaza de los Fueros and Calle Pintorería.