Get your tickets and join the fans at a game at Rheinpark Stadium. If there's nothing happening while you're in the area, you might like to check if they give a tour of the facilities.
You're spoiled for sightseeing choice in Vaduz. Rheinpark Stadium is a great place to start here, but there are numerous other fine spots to explore. Vaduz Castle, Malbun Ski Resort, and Liechtenstein Art Museum are not far from the sporting facility and and will cap off your day nicely.