The City Backpacker Biber in the middle of Old-Town Zürich is a nice and cheap place to stay: www.city-backpacker.ch The youthhostel is unfortunatly located a bit outside of Zurich but you can reach the City easily by public transportation. about 10 years ago
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 10 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 8 years ago