Most of the tourists use Irkutsk as a stop over destination on their way to lake Baikal. This is good, nothing wrong about it. The wrong thing is that tourists do not pay as much attention to it as a City. It deserves minimum 1 full day of your time or better 2 full days.
It has beautiful historical city center which is perfect to explore by feet. Please use the GREEN LINE city walking route. Besides of that, you can add another day to see other site which most of tourists do not see: the RED LINE additional walking route.
View Green Line in a larger map