Hi!
That's a good time to be in the North. The begining of october is likely to be rainy everywhere...except for the North, which usually has nice weather during the start of fall.
Expect temperatures to be around 65 in the coast (55 by night)
The Pyrenees will be a lot colder, specially Ordesa which is high mountain, and up there the weather won't be so nice, it even snows that early some years.
It looks like you are interested on nature and landscapes.
If you have time, betweem San Sebastian and Jaca there are plenty of gorgeous unspoiled valleys, from west to east:
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Baztan, typical Basque valley , green and peaceful.
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Salazar, huge woodlands.
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Irati, the biggest beech wood of western Europe.
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Roncal, ancient valley with interesting
architecture and the first in which the high mountains begin.
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Hecho and Anso, very interesting valleys because of their nature and their quiet towns.
From Jaca you can explore
Valle of Aragon, with the Canfranc international Station and
Valle de Tena, beautiful wide alpine valley full of lakes and 10000 feet peaks. Theese last two are more spoiled and touristy, with four ski resorts.
From there starts the road to
Ordesa, one of the most beautiful National Parks in the world.
