WiFi zones can be seen in a cafe on the Ondarreta beach; in many bars in the Old City. It's unclear whether they are paid or free of charge.
C/sanchez toca, 7. in the centro neighborhood, right behind the buen pastor cathedral. offers free wifi with purchase of food, drink, etc.
C/ijentea, 4. in parte vieja, towards the end of the boulevard, going towards the kontxa. offers free wifi with the purchase of food, drink, etc.
There are many WiFi points throughout the city and indicated by a white WiFi symbol on street-posts. These are free to access.