Another of the high alps golfing experiences is at Verbier Golf Club, a famous ski resort town. We had a Swiss Greenkeepers Association meeting there a few years back. The first tee sits hundreds of feet above the clubhouse, which you get to by shuttle, and you traverse your way back and forth down the mountainside with spectacular views up the Vallee du Grand Saint Bernard towards the big peaks of Chamonix namely the Mont Blanc. I learned quite quickly that it wasn't smart to miss fairways. On the second hole, a par four, I missed the fairway left. I had to mountain goat my way down to my ball 50 meters below the fairway just to get my ball back in play. It isn't a great round of golf, but it is a fun and different way of hiking the alps.
The alpine villages are quite charming on their own, golf aside. Having spent several years there, my personal choices are Ascona, Lausanne and Domaine Imperial (personal favorite). All three suffer from claustrophobia, in areas. Unfortunately, the countries best courses suffer like much of Europe, with over watering and an obsession with green grass. I do think Ascona could be a fantastic golf course with the proper renovation, with it's spectacular location on Lake Maggiore.