They're even available at some laundromats. They're everywhere.
What you want to do is find an internet cafe that has prime time hours and off hours. During the peak hours, it costs less to use the computers. During the off hours, they charge a little bit more. And you can buy time in advance and then use the time up as you come and go (this is if you plan to be in one city long enough).
Or just find a laundromat that gives it to you for free if you wash your laundry there.
I don't know about hostels but computer cafes were not hard to find last summer in Italia. I was in some fairly small towns and they had them. I think it was about €5 for a half hour. I was on the Amalfi coast and on the islands off the coast of Naples.
Lavanderia were *much* harder to find than internet cafes! In fact, I never found one! Ended up hand-washing my stuff in the bath.