Get your tickets to see a game at Baikal Arena. If there's nothing scheduled while you're in town, you might like to check if they give a guided tour of the facilities.
If you're staying a while in Irkutsk, Baikal Arena is an interesting place to start your sightseeing. This sporting facility is one of many attractions that'll keep you on the go here. Kirov Square, Znamensky Monastery, and Church of Our Lady of Kazan are also waiting to be explored nearby.