Irkutsk has many places along the central Karla Marksa Street, there are many restaurants and cafes like Italian pizzeria, Chinese and Japanese restaurants, and Swiss bakery, that's where most of the people go out anyway, and the food is great and inexpensive.
The thing to try in Irkutsk is "Bliny", which is the name for Russian pancakes. They're made of pastry with eggs, and often have delicious fillings inside, like cottage cheese, jams and baked fruits.