Try the lake. Jokes aside, this being Switzerland, there are people in Zurich who'd park their car in Lausanne if it were free. There is an international boarding school up on the hill...and if I were you, I'd try to talk to them to see if they are willing to let you leave it for 3 weeks (even for a small fee)....as parking anywhere in the world is becoming more and more like an extreme sport.

pm me for the contact information....if interested.