There are loads in the Cordillera Cantabrica. I have ridden offroad between Santander and East of Jaca with no problems. If you come across a prohibited sign just find an alternative nearby. There are more prohibited signs nearer the French border and obviously at the Natural or National Parks.
I plotted routes from a Spanish 1:50k map and went from there.
Be warned : the "white roads" shown on the maps can vary in reality from wide tarmac roads to rabbit tracks where the roads haven't been used for many years and are well overgrown although you can still just make out the outline. For example, we took 3 hours to cover 6km in one instance : great fun !
Good luck and enjoy