I know this isn't what you want, but I think you should have at least a couple of different bases for your month. You could stay places for ~10 days which would involve minimal moving, and it would be a tremendous amount easier to explore the region from there. Especially without a car rental.
Even with a car, if you pick a central location, you could be 6 hours from Porto or Lourdes. By public transportation, you could be a couple times that, or more if you want to avoid staying in a larger city.
My suggestion would be to stay the 1st 10 days in Porto or Santiago de Compostela or Vigo as base. Then spend the next 10 days with base of Leon or Oviedo or Santander. Then make San Sebastian your base for the last 10 days. That will cut down on travel distance tremendously.