My sister is here with us for 3 months. 88 days to be exact. Can she open a Post Finance account with only her US passport? Does she need a residence permit? I don't know because I had them when I moved.

According to the end of this thread, it sounds like they are now requiring residence for non-Swiss Postfinance account for non-resident (tourist)

Other banks might be more lenient (definitely not UBS, probably not credit suisse) - if she did get one open, remember that she would need to fill out the FBAR for the IRS if the amount is above 10,000USD at any point during the year (I'm assuming she's American)

She can probably open a savings account in the Cantonal Bank, and don't tell Uncle Sam!

She would require a residence permit.

FBAR is when a bank account or combination or bank accounts exceed
$10,000. Otherwise, she would be exempt.

It didn't work so well for Julian Assange but he was a special case....