Irkutsk's City History Museum gives a compact overview of the city from its early settlement through its role in Siberian trade, exile, and regional culture. It is most useful early in a visit, before walking the historic wooden-house districts and central streets.
The displays are local rather than blockbuster, but they help explain why Irkutsk became one of Siberia's key cities. Allow enough time to connect the museum's historical context with the architecture and monuments around the centre.