I think that Irkutsk is an indispensable part of a trip to Russia. Irkutsk will definitely surprise you. It is near Lake Baikal, on a cultural crossroads (Russians, Buryats, and Mongols), and with a past that is as fascinating as it is rich. So get 100% out of the town and don't rush off to see the lands around Lake Baikal too quickly!
Walking along the banks of the Angara, visiting the many magnificent churches, or the houses of the Decembrists (intellectuals who were exiled for revolting against Nicolas I), helped me to understand how the city has benefitted over time from an important and rapid cultural, artistic, scientific, social and political development. Its rich history is reflected in the architecture, and when you have walked around, you feel deeply affected by the city, even though it is so far from the Russian capital.
Take the time to visit Irkutsk properly, and also to go round some of its many, enormous and typically Russian markets. It's a Francophile city, so if young people don't speak English they may well speak French!
Apart from the difficulties of pronouncing its name, Irkutsk is a small but pleasant town. And it's already got the benefit of being next to two great Russian must sees - the Trans-Siberian and Lake Baikal. But I was surprised to find how many beautiful pieces of architecture there are, especially the churches.
I was really wowed by Irkutsk Cathedral, as well as Prince Vladimir Monastery. The towers, onion domes and wonderful colours are real works of art. During a trip to Russia, lots of travellers spend more than a week travelling the continent from Beijing, Ulan-Bator or Vladivostok but I really recommend you stop for a few days in Irkutsk and spend time in the wonderful countryside around the sublime lake.
I got off the Trans-Siberian at Irkutsk and I wasn't disappointed. The town doesn't have many interesting things to do. I enjoyed walking through the 19th century buildings and the many small churches. It has been welcoming tourists for a few years so there are plenty of places to go to stay or to enjoy yourself.
There are a few museums, as well as Znamensky monastery and Epiphany Cathedral to see, but I didn't stay long in Irkutsk because it's quickly seen. I made the most of being there by going to see Lake Baikal , which is only 70 km away. The world's largest fresh water lake is the must see of the region and my detour there was more memorable than the town of Irkutsk itself.