The Stubaital glacier region just south of Innsbruck is very nice. Mieders is a great little village on the way. Stay there in the hotel/apartments just above the Spar grocery store.
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Another great drive is the B roads north of Innsbruck over to Garmisch Germany. The 1936 Winter Olympic stadium is still there with the ski jumps.
Sorry for the overkill on Garmisch. Missed that part of the OP. Still a great drive over the mountain.