I'm sorry but I can't help you, cause I've been there on camping many years ago. I think that things are changed...
Anyway try this:
http://www.hostels.com/findabed.php?ChosenCity=Zurich&ChosenCountry=Switzerland&Search=1 about 8 years agoAnswered by gianluigi bombatomica via Travellr.com
The word "cheap" and "Zurich" don't belong together ;-) but I would recommend to have also a look at the chain hotels like ibis from Accor. There's one here
If you more an explorer you don't spend much time in the hotel anyway. It is clean, simple and offers good money for value.
Or this as an independent one
http://www.greulich.ch/konzept-greulich/en/hotel_restaurant_bar_zurich_city.aspx over 6 years ago