I've stayed at two there.
http://www.redhostel.com/ The Red Hostel, which is fairly cheap and I enjoyed to an extent. The only problems were it's location away from the historic area and groups of young people that were there to party. Nice rooftop terrace and decent breakfast along with free internet make up for it.
I also stayed at http://www.ciudadviejahostel.com/ which is near the historic area and a place I enjoyed. The advantage here is that it's close to restaurants, bars and sights in the historic area. The downside is that this area may be considered a bit more dangerous although, I never had any trouble. More of a laidback feel to this hostel while I was there and they include internet and breakfast as well. I would go back there rather than the Red Hostel if I went back.
A couple other options as well.