Dang, somehow the message I was typing disappeared, so I'll summarize it.
For the cities, I'd swap Burgos for Valladolid anyday...I've been to both.
"cities with a lot to offer = mass tourism" is mostly a fact of life. Like Jer says, June is better than later in the summer.
Maybe you might consider a two-prong approach: time spent in cities, with time in more tranquil, natural areas in between.
Here's what we did in early May a few years ago: Visited "heavily touristed" Santiago de Compostela, then rented a car to drive across Spain for a week. We dropped the car off in Bilbao, saw the Guggenheim Museum, then took the night train to "heavily touristed" Barcelona.
On our drive, we loved the Picos de Europa's mountains and valleys, as well as the coastline and beaches of Galicia and Asturias (we were blessed with good weather). In the cities, we loved the nightlife, cathedrals and museums. Both parts were great, but different; I wouldn't have eliminated either.
IMHO it would be a shame to pass up on all the great art and culture that cities have to offer, just because of crowds. With some planning you can overcome the big city tourist hassles.
For example, we ended up seeing museums early in the morning, and cathedrals when others were eating lunch.
just my 2 cents.
"An honest man is always a child" - Socrates ...no wonder I'm so immature!