Bayonne is right next to Biarritz. Stay in Biarritz and take a short drive to Bayonne. Biarritz has lots more to see than Bayonne. In fact, you may find it hard to leave Biarritz. I suggest a day trip up to the mountains, to Saint Jean Pied de Port. Of course, this is all France, not Spain. By the way, do stop in Burgos at least for lunch, or better yet stay one or two nights. It's a great place. Sounds like a great trip--but it might be easier and more fun with a rental car.