Buy a ticket and join the fans at a game at OlympiaWorld. If there's nothing scheduled while you're in the area, you might like to check if they offer a tour of the facilities.
You're spoiled for sightseeing choice when in Innsbruck. OlympiaWorld is a great place to start here, but there are loads of other worthwhile spots to appreciate. Golden Roof, Bergisel Ski Jump, and Imperial Palace are near the sporting facility and will round out your day nicely.