How many days do you have?
I like Bilbao better than San Sebastian. It's much less touristy and has a larger historic district, plus several art museums. Of course, San Sebastian has that gorgeous beach. (Weather doesn't always cooperate, however.)
The interior capital of Vitoria-Gasteiz sees few tourists and has a large, picturesque, hilltop historic district, plus a couple of art museums.
Hondarribia is a coastal town almost on the French border with a fishermen's district (restaurants) along the water and historic district uphill.
There are some cute former fishing villages (now touristy) stretched out along the coast between Bilbao and San Sebasian: Zarautz, Getaria, Zumaia, Lekeitio. Bermeo near Bilbao is also worth a stop.
The Basque countryside is very pretty. I recommend not spending all your time right along the coast. If you go to the ViaMichelin website and really zoom in, the especially scenic roads will be highlighted in green.
Olite is a back-of-beyond town with an impressive castle. It feels very different from the Basque country.
Pamplona is well within your range. There are many, many cities in Spain that I prefer. Check timing of the running of the bulls. I know the city is beyond filled up during that period.
The La Rioja wine area may be within 2 hours of San Sebastian. I am not a wine person and do not actually know where La Rioja is.
