There are a few good hostels around town, but I am not going to beef up hostels I haven't visited.
Che Legarto is one of the gems just off of the Plaza de Independencia. The building is gorgeous, and the crew there has really done up the hostel nicely. They are an accomodating, friendly, and very helpful hostel.
Posada al Sur is another very cool spot, and a bit further into "the dangerous" Ciudad Vieja (but it is not really dangerous, just don't be dumb and walk at night with a flashing digital camera, a rolex watch, and an Ipod, for example). The atmosphere is very relaxed with open rooms and a big comfortable kitchen. This is a favorite for me.
There are a few other hostel choices as well: Red Hostel, Viajero, etc., but I have not entered them yet.