The iconic domes of Kremlin in Moscow are supposed to represent the turbans of defeated Turkish sultans. So they are deliberately kinda middle-eastern, even though Russia is a different animal altogether.
Not meaning to throw any flames, but I don't think this is correct. From what I've read the shapes come from religious design and have nothing to do with defeated sultans. :)
As for the middle eastern influence...everyone from Mongols to Nazis' have invaded, occupied or pillaged the people and countryside of Russia. Their buildings show many different influences.