Innsbruck was forgetful, I wouldn't focus any attention on the town itself. It's small, boring, and not particularly pleasant. I had this image of an alpine oasis before I visited, which was quickly disproved. However it's known for hiking/winter sports so that side may be impressive.
The city topped a TripAdvisor destination of the year list a few years back, it definitely gets raved about. I was considering going but then there was a bomb blast at the airport which made me reconsider. Just seems to be in the thick of numerous political hazards of late.