The Alpina Gstaad is a true five star gem. We stayed there last September and loved it. Service especially was amazing. However, we found the town, while charming enough, to be somewhat sterile focused mostly on uber high end shopping befitting the winter clientele. Also, the scenery was pleasant enough but lacked the in-your-face drama of Zermatt or Saas-Fee where the mountains and glaciers loomed everywhere.

In Grindelwald we stayed at the Boutique Hotel Glacier. Fine enough but far from five star.

While, personally, I have no experience, a Six Senses property recently opened in Crans Montana. You may want to investigate it.

Outside Lucerne on the lake we stayed at the Burgenstock. I know that PHV gots all the love on this thread. But we found the B’s perch high above the lake with its cantilevered pool to be stunning. Also, the B has a funicular that takes guests down to the lakefront where a shuttle boat will take them directly across the lake into town.

It may not be geographically optimal for your itinerary, but our favorite Swiss mountain village is Zermatt. The Matterhorn towers over the village. We love the Omnia here. While perched above the village, it has a wonderfully engineered lift that drops you into the center of town. Great personalized service too.