Oh knowledgeable ones on this forum:

We live near Lausanne, but after our experience flying from Geneva to San Francisco via Heathrow before Christmas, the Swiss Air non-stops from Zurich to SFO are looking better and better.

According to ifly.com, "Many local hotels offer up to 2 weeks free parking with one night stay. This can be especially convenient if you have an early flight and need to park at Zurich airport. They provide shuttle service too."
Unfortunately, ifly.com does not identify the "many" hotels making this offer.

Through extensive googling, we've been able to identify two hotels offering such an option: Zurich Moevenpick (up to 2 weeks free) and Zurich Renaissance (up to 1 week free).

Does anyone know of other hotels near the Zurich airport that offer free parking after you stay one night?

Thanks for your help!