It will probably be terribly costly to pick up a car in Spain and drop it off in Portugal--but perhaps that's not what you are planning to do.
What time of year is your trip?
Jaimeelsabio has seen more than I have, but I can add that the inland cities of Burgos and Leon are historic, pretty and lively. Within Galicia I liked Pontevedra and A Coruna in addition to the obvious Santiago de Compostela, plus the smaller towns of Betanzos, Combarro and Cambados. The inland border town of Tui is worth a stop, but the direct driving route from San Sebastian would cross the border east of Tui (also missing all the other places we've mentioned in Galicia). Vigo is imminently skippable.
In the Basque Country I liked Bilbao and Vitoria-Gasteiz even more than San Sebastian, but I'm not a beach-goer or a gregarious bar-hopper.
The Picos de Europa area is dramatically pretty. I just took a bus tour there so can't provide specifics beyond saying that the old stone town of Potes is touristy but handsome. As you would expect, there roads there are windy; don't expect to make good time in that area.
The Basque Country is also lovely.
From your reference to "a few days", I gather that you don't have a great deal of time. You may need to focus more on scenery seen on-the-go and some convenient stops mostly in small towns. Visiting places like Bilbao, Vitoria-Gasteiz, Burgos, Leon and Santiago de Compostela may slow you down too much. Those are all places where an hour or two might be more frustrating than enjoyable.
If you decide on the inland route that takes you past Vitoria-Gasteiz, you'll be near the very atmospheric small hill town of Laguardia, which sits near the La Rioja wine country.
I tossed each chapter of the RS "Spain" book as I left the area and don't remember exactly what is covered, but I think there's info on at least SS, Bilbao, the Picos de Europa, Burgos and Santiago de Compostela. I just checked Amazon and found a Lonely Planet book that may cover more towns (but in less depth). There are DK Eyewitness Guides to both Spain and Northern Spain--too heavy to travel with in my view, but good for advance research.