I walked along Santa Monica Blvd from Fairfax to La Brea, visiting all of the Russian bakeries, delis, and groceries along the way. I had no idea how many of them there are, at least a dozen, most of them small. On the whole I was a little disappointed. There's nothing that comes close to the total immersion in Russian culture that you get on Brighton Beach Blvd in Brooklyn. I was particularly disappointed by Stolichnaya Bakery, next to Whole Foods, whose cookies and pastries seemed tired. (I didn't try their bread, though, which others have recommended.) So I didn't end up doing as much sampling as I had wanted.
The most interesting place was the Tbilisi and Yerevan Bakery (7862 Santa Monica Blvd, (323) 654-7427), which someone mentioned here recently, though I guess it technically isn't Russian. There I got a cabbage pierozki and a triangular poppy seed pastry. The pierozki actually turned out to be mushroom and egg rather than cabbage. The bread part had a pillowy quality that could have been good with the right filling, but the mushroom and egg didn't work out that well. The poppy seed pastry, on the other hand, was excellent, with fresh and moist poppy seed filling and flavorful pastry. It was probably better than at places like Schwartz Bakery to the south.
If others want to visit these places, what I would recommend is to start with the Tbilisi and Yerevan Bakery, which is on the SE corner of Santa Monica and Fairfax, and walk several blocks east along Santa Monica, staying on the south side of the street. The delis on the south side seemed generally happier than those on the north, and they are reasonably close together.