I'm still writing up my trip report for the Basque country in May 2017, but here's a preview. I had one night in Vitoria, and saw:
a) Some of the archeology museum (free). Only some, because descriptions are in Basque and Castilian only, and, while there is a free English audioguide if you know to ask for it, only a few items had audio descriptions.
b) The playing card museum, in the same building as the archeology museum (free). Very interesting if you are into this sort of thing. Don't miss the Kamasutra deck, or the one owned by the Sforza-Visconti family made of parchment with gold leaf. Here, the audioguide covers each room - very helpful.
c) The Museo de Bellas Artes, or Fine Arts Museum (free). This is fantastic - I rarely call anything a must see, but if I ever did it would be this. Not only was it filled with my favorite kind of art - great stuff that I've never seen before, by artists I've never heard of, so it's all a surprise - but it had only a few other visitors, so I could enjoy everything in solitude.
d) The Artium, or modern art museum (€5). This had four exhibits, three of which I liked and one of which I found only OK. However, I still felt visiting was worthwhile (although an inevitable comedown after the Fine Arts Museum). In addition it has longer hours than the other museums (the reason, with only one day, that I saw it last).
Note that all of Vitoria's museums (the town's tourist brochure lists 7) are closed on weekdays from 2 to 4 PM. All but the Artium reopen from 4 to 6:30; the Artium reopens from 5 to 8. I do see from their website that the Artium has no midday closing on Saturdays and Sundays, but some others are open shorter hours (morning only) to compensate. In addition, all seven museums are closed on Mondays.
The upper old town of Vitoria may be pretty, but it was pouring rain when I was there so I wouldn't know. Fortunately it had stopped raining when I saw some of the lower town (the commercial center), which has some pretty areas as well.
If you're looking for a hotel in Vitoria, I recommend the Desiderio (http://hoteldesiderio.es/ - use Google Translate if needed). It's a block from the Artium (and its taxi stand, very handy for getting back to the bus station) and 5 minutes from the Bibat, which is the combined museums of archeology and playing cards. My single room was a steal at €35 per night.
SO, if you're as interested in the museums of Vitoria as I was, two nights would be very good, so you won't rush around as much as I did. If you're not as interested, or if you're there on a Monday when they're closed, one night is probably enough.