When someone tells me they're traveling to Spain and looking for recommendations; San Sebastian (Donostia, in Basque) is my first thought for city destinations in the northern part of the country. It's charming, beautiful, and steeped with history. Mount Urgull, the hill that stands on the right side of the bay, epitomizes all those characteristics in one easy to explore package.
Mount Urgull is an easy walk from anywhere along the Promenade and you can either walk up from Parte Vieja or walk around the by the aquarium and the point to see views of the Bay of Biscay. I'll recommend that you start with the second way and on your way back down, drop right into Parte Vieja. That way you get the best of both.
As you start your walk up Mount Urgull, you'll get beautiful views of the Bay of Viscay and historical sightings right away. I believe the building on the right used to be a storage depot for armaments. One of the things I found fascinating about Mount Urgull is the layers of military history built upon it. Since the founding of the city in the early 12th century, it's been used for military defense - so you'll see French built battlements, an English Cemetery, and more.
Perhaps one thing I loved the most about the views from the Basque Coast was the ruggedness - the high cliffs and beautiful pine trees remind me of the Northern California coast.
One Mount Urgull's major selling points in terms of visiting, is the views of San Sebastian. From the remains of Napoleon's contribution to the structures on Mount Urgull, you get a wonderful view of Isla Santa Clara and Mount Igueldo across the bay.
Continuing along the walk up Mount Urgull, you'll find a lovely area with picnic tables to have lunch with amazing views of Playa de la Concha, the city, and the surrounding mountains.
Eventually, you'll find yourself at the base of the 12th century La Mota Castle with much more to explore. Follow the stairs up and down various pathways to see different levels of the Castle. Make sure to admire both the historic cannons and the views as you explore.
There are a number of benchs and places to sit in the castle, making it a great place to just learn back and read a book. It would also make a wonderful place for a picnic lunch.
Before heading back down Mount Urgull - make sure to walk out to the farthest point to see more remnants of military history and a wonderful view of Parte Vieja from above. Oh and don't forget to take a moment to admire the huge Basque flag flying above!