My recent trip to Russia started with a lot of apprehension about the availability of vegetarian food in Russia, which is predominantly a meat eating country. I was pleasantly surprised at the variety of vegetarian food that was available. I wouldn’t say that we were spoilt for choice but there was enough around, for us to not have to eat similar stuff every meal.
Teremok, is a chain of fast food joints , very popular in Russia and their most popular dish is the Blini, which are like soft crepes and come with a variety of fillings . There are a couple of vegetarian options with mushrooms etc and the most interesting part is that they come in both savoury and sweet fillings. The Blinis are made right there in front of you and that’s very interesting.
In Saint Petersburg, we ate at a completely vegetarian restaurant called Botanika. They also had a fairly large choice of vegan dishes and to our utter surprise had a couple of Indian dishes also. Their most popular preparation is the beet root soup called Borsch. 
Buck wheat Blini 
khachapuri is another famous Russian snack which is like a stuffed puff with a variety of vegetarian and meat fillings. We sampled mushrooms and potato stuffed mushrooms ones.
Cheburek is another snack vegetarians can look out for which is also like a puff pastry . This one also had a mushroom and potato filling
Besides these Moscow had a lot of Italian and fast food options.