Having to work makes a lot of difference. If you want a spot on the French side, I'd vote for Bayonne since there's more to see there--a large historic district, an art museum, a chocolate museum with a very generous tasting room. Others would prefer St-Jean-de-Luz, which is smaller, which has its own appeal. I just get stir-crazy if I'm stuck in a small town for very long.
I much, much preferred Bilbao to San Sebastian. Bilbao has more to see, including a large medieval district, and is far less touristy. But San Sebastian has the magnificent beach. I suspect your kids will vote for the beach. The train between the two cities is considerably slower than the bus (or a car), but it runs through some very pretty countryside and is worth taking.
I really didn't care much for Santander. It's not a bad or unattractive place, and it has lovely beaches. But there was a dreadful fire back in the 1940s, and there's not a lot of historic architecture remaining. A plus for Santander is that you could day-trip to the dramatically beautiful Picos de Europa area. I know that, because I took a one-day bus tour from Santander.
Farther west your choice of good-sized places comes down to Oviedo and Gijon, I guess. Oviedo is an historic city with some extremely old (and important) churches. The city itself seemed quieter than one would expect in Spain. I remember reading that the locals go to Gijon for excitement. Gijon is an industrial, port city. It has a very small historic area and some attractive early-20th-century architecture.
Really, where you should stay depends to a considerable degree on what side trips you think you'll want to make. I used public transportation, so I don't have an innate grasp of what places are workable from various bases.