First of all, congratulations on your marriage! This sounds like a nice honeymoon.
I just got back from Spain a couple of months ago and hiked/camped a few days in Picos de Europa National Park in the extreme north-central Spain. We ddn't do campgrounds, just stopped when we were tired. Actually didn't see any campgrounds. (I don't do campgrounds in the USA either). We rented a car to drive to this remote gorgeous area.
For the remainder of the 16 days, we used the wonderful train system to get around the country. You can get to any major urban centers by train but the rural areas means buses or hire a car. BTW, they don't speak English in Spain except occasionally in Barcelona.
"Life is a Project!"