The north of Spain is not the Spain you may have in mind when thinking about Spain: no bullfights, no flamenco, no olé, no palm trees, no white dashed houses, nothing of that kind (you will find that in southern Spain). Instead, the north is what we call 'the green Spain'. The landscape can be described as a mixture between France and England, green, cloudy and rainy most of the year (don't be afraid, you will find sun in June but be ready for some windy days).
The north of Spain is a well known destination among spaniards, specially in summer when everywhere else is suffocating hot.
There's a strong celtic heritage, stronger at the west. People can be surprised to find pipe players, skirts and folk music which reminds of Scotland.
If you have never heard about the 'Camino de Santiago', the route from France to Santiago used by pilgrims during centuries, I suggest you look for some information about it. It's very famous. Here's the official site:
http://www.caminosantiago.com/web_ingles/index.htm
I suggest you travel along the 4 'Comunidades Autónomas' in North Spain(semiautonomous regions, similar to the states in USA but with a strong historical identity): Galicia, Cantabria, Asturias and Pais Vasco/Euskadi -Basque Country-). This also means dealing with 3 of the 4 official languages in Spain: spanish, galician and basque.
You wont find big cities. The charm of this part of Spain is to explore towns, small villages.
The musts: Santiago de Compostela (Santiago de Chile was named after it ;-) ) and San Sebastian ('Donostia' or 'Donosti' in Basque language), add also Bilbao to the list because of the Guggenheim.
Other places: Santander, Covadonga, La Coruña, Pasajes/Pasaia near San Sebastian, the whole coast and a neverending list of small villages including Santillana del Mar.
Beaches: Santander and San Sebastian
I recommend you renting a car and explore at your ease.
Otherwise:
By bus:
http://www.alsa.es/ to Galicia
http://www.continental-auto.es/ to Basque Country
By train:
http://www.renfe.es/
More:
Galicia: http://www.turgalicia.es/
Asurias: http://www.infoasturias.com/
Pais Vasco: http://www.paisvascoturismo.net/
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