There are some great possibilities to spend time in Zurich without spending a franc:

Dance at the Cool Monday party at Mascotte and only pay for your drinks.
 Tuesday is concert night at La Catrina and the bar of Hostel Langstars. There is no entrance fee, only a small donation for the local bands is expected. 
On Wednesday afternoons you can visit the Collection of the Kunsthaus for free
.

Rent one of the free bikes at the stands of „Züri rollt“ and discover Zurich by bike. 
If you understand German, check the city department of cultural heritage preservation, they offer free tours.