We just spent a wonderful week at the Post Hotel in Leermoos, Austria (Hotel Post Lermoos: Hotel Post Lermoos). Skiing and Cross-country skiing was superb. The Post Hotel is a real 5-star gem in the winter as well as in the summer. I wish LL would add this property to its list.
In the summertime, you can enjoy endless hikes and excursions or golf in the Zugspitz Arena, and Innsbruck is just a shorth drive or train ride away.