Don't get stuck on campus or at the whim of ZipCar availability.
My Mazda3 is available for rent on Turo for the day, week, or month - all insurance is provided through the site.

https://turo.com/rentals/cars/ca/stanford/mazda-3/442662?searchId=NHpRtnJ0

It has campus tags and can park in any C lot on campus.

You get $25 credit when you use the link below:
https://turo.com/c/jonathank766

($7 price base off one day usage with applied credit)