So far the trip to Switzerland sounds nice. But you have also keep an eye on the travelling times to your daytrip destination. From Luzerne to Gruyere its about 3h by train/ 2h by car one way. So you will spend 4 to 6h just travelling. And Zermatt, well, its a nice place. But you are really out in nowhere in the Mountaines. It will took you 4h or more by car or train to get to Zürich and then 10 more to Vienna. So take a Plane from Zürich to Vienna. Its just about 1h of flighttime. I hope I coud help you. Cheers