Thank you for the information regarding it's not allowed to spend the night in the Airport!
And Stout - that's the cheapest hotel so far - thanks!
I've just tried calculating what it will cost us, if we rent a car here in Yverdon and leave it at the airport for the weekend.
All in all it will be approx 120CHF, and because we don't have to buy traintickets, it will only be 55CHF more, than taking the train and finding a couch to crash on. Then we can drive early in the morning and be there in time.
But I will definately just check couchsurfing again - fun way to meet new people
Thank you for all your help!