Congrats on the new addition!
It might help if you said where in Zürich you are, and how far/which OV lines you'd consider reasonable to travel.
I am not in ZH, so can't be much help there, other than to mention one place every pet owner in the greater Zürich metro area should know, the University of Zürich Tierspital:
https://www.tierspital.uzh.ch/de.html
This is where you might need to go in an emergency, or if referred for specialist treatment. It is one of the premier vet schools in Europe, a resource we are all very lucky to have access to.
While the clinic does indeed offer regular primary care, you likely will want a private vet as your primary carer, if only for the personal relationship. Hopefully someone in ZH will be along with recommendations.
But when you need the 'bells and whistles' the Tierspital is the place to go.
(After hours emergencies call first; for specialist consultations generally you should have a referral from your primary vet.)