Mathemilu, I'm confused. Are you traveling with bucephale? If you are not, you should start your own thread, because it's very confusing when people start giving responses for two different itineraries.
In northern Spain, in addition to the cities already mentioned, I liked Burgos and A Coruna. The latter has a sunnier-than-usual microclimate, however, and I cannot promise that it will be cool like most of Galicia in July. There are scattered picturesque former fishing villages (now mostly touristy) all along Spain's northern coast. When you pin down the cities you plan to visit we can probably suggest some nearby options. I visited five small towns/villages in the Basque Country alone, and they were all worth a stop: Hondarribia, Zarautz, Getaria, Zumaia and Bermeo.
The Picos de Europa area would be a good possibility in the summer, too. It's mountainous and cooler than places farther south. Possibly warmer than the coast when you're not at altitude, though. Just driving through that region is beautiful. I especially I liked the historic stone town of Potes.
I enjoyed an afternoon wandering around Gijon, which has a small medieval district and some interesting early 20th century architecture. It's a large industrial city, though, and I don't know how easily you'll get around with a car. One thing to check on if you're trying to avoid unnecessarily costly hotels is the timing of the annual large literary festival held in Gijon, Semana Negra. It's not a terribly touristy city, so I'm assuming things get very tight during Semana Negra.
Zaragoza bakes in the summer. Nearly as hot will be the smaller town of Teruel, which has distinctive architecture with both mudejar towers and quite a bit of modernista stuff. Teruel is time-consuming to reach, but it's not so bad if you'll already be in Zaragoza, and I found it extremely atmospheric and with comparatively few non-Spanish tourists.
