There is a lot of internet-access along the camino.
I got a list from another member on this forum- "Sillydoll"
you can send her a mail and ask for it [edited: ivar, see below].
Then I think she will send you a mail with the list
And the prices can be from 1E for 15 min, to 1E for 1 hour.
The internet-boxes in the refugios can be expensive AND occupied! So look for internet at cafetería or local bars.
[edit: I think it is best not to post 3rd persons e-mail addresses on the forum, due to the fact that this person probably will get exposed to more spam. To get this e-mail address I suggest e-mailing bsaa77 (e-mail icon below this post. This icon is visible to members only and is therefore spam safe)]