Thank you. We should have a few people knowledgeable about driving in the Pyrenees, and the date will help them.
I'm one of those who preferred Bilbao to San Sebastian. It's less touristy, has a larger historic district and more museums. Foodies and those looking for a super-lively tapas scene might be happier in San Sebastian. I hate changing hotels, so I'm not going to suggest that you split your time. I did so, but I had more nights to divvy up. I just want to note that you can easily spend more than a full day in Bilbao if you like art., and there's a lot of walking around to do even if you don't.
Vitoria-Gasteiz is also very interesting. The historic district is on a hill, but there are outdoor escalators to assist you when you want to change levels, so it doesn't have to be strenuous. There are a couple of art museums outside the historic district and a playing-card museum inside it. As of 2016 the public-transit card used in Bilbao also worked in Vitoria-Gasteiz. That was a pleasant surprise but handy.
I didn't find Pamplona special at all. There's a small historic district, and a cool life-size running-of-the-bulls sculpture, but it seems to me that there are many more interesting places in Spain.
I'm a public-transportation traveler and haven't visited the Spanish Pyrenees, but I spent several days in the Cerdanya Valley. The large town of Puigcerda (virtually on the French border) is very colorful. There are some old towns nearby that are worth 1 to 3 hours of walking around just for their atmosphere: Llivia to the north on N-154 (actually surrounded by French territory) is the largest. Bolvir, Bellver de Cerdanya and Martinet are to the south along N-260 and smaller. Note, though, that this valley can be miserably hot in the summer, and you may be unlucky in that regard. At least you'll have a car (air conditioned, I trust) to retreat to.
I also thought La Seu de Urgell had an especially pretty historic area. There's also an important cathedral.