Hello dugurugu
Firstly, welcome to the SBB Community.
We suggest looking at the validity map available on the product website in the ‘More on the topic.’ box:
https://www.sbb.ch/de/hilfe-und-kontakt/produkte-services/swisspass.html#anchor4
As you can see there: YES, the pass is valid even for city transit.
However, Zurich is not well located to do day trips. If you can you should reconsider your base and change to a place which is more centrally located, such as Bern or Lucerne. And, Zurich is expensive > might to be considered if you are on a budget travel.
Kind regards,
Roland