I currently have a bank account with UBS and another with PostFinance. I prefer to have two accounts for redundancy and to avoid having too many assets with UBS (where I also have a mortgage).
The UBS costs are minimal due to reduced fees from having a mortgage. PostFinance was previously free but have increased fees to 5 CHF or 25 CHF per month.
Looking at alternatives, today, I found https://www.neon-free.ch which appears to be free (although in BETA and missing some key features) but having the bonus of English language.
ZAK is run by Cler, and appears to be mostly free (not too easy to get the info) but perhaps this will change. They currently also give a 50 CHF signing bonus and have a referral offer: https://www.cler.ch/de/landing-pages/zak/