San Sebastián is exceptionally well-placed for day trips. Bilbao (100km west) and the Guggenheim Museum is the obvious big trip — allow a full day. The Euskotren coastal railway offers a more scenic alternative to the motorway and stops at several interesting towns along the way.
Getaria (30km west along the coast) is a stunning little fishing village on a rocky peninsula, with some of the most dramatic coastal scenery in the Basque Country and the txakoli wine vineyards on the slopes above it. Getaria is also the birthplace of Juan Sebastián Elcano, who completed the first circumnavigation of the globe. The Balenciaga Museum here, opened in 2011, is outstanding.
Hondarribia (20km east) is a beautifully preserved medieval walled town at the mouth of the Bidasoa river, facing the French town of Hendaye across the water. The old town within the walls is largely traffic-free and almost untouched. The Basque French coast — Biarritz, Saint-Jean-de-Luz — is just 30km north and makes an easy half-day excursion.
Rioja Alavesa wine country is about 90km south: the bodegas of Laguardia and the landscape of the Sierra de Cantabria make a superb day out, especially with a car.