Purchase tickets to watch a game at Taoyuan Arena. If there's nothing happening while you're there, you might like to check if the stadium offers a tour of the grounds.
You'll have no end of sightseeing choices when staying in Taoyuan City Centre. Taoyuan Arena is a great place to start here, but there are many other fine spots to explore. Chung Yuan Christian University, Taoyuan Night Market, and Sanxia Old Street are close to the sporting facility and will round out your day nicely.