I did get a little bit of detail about my eastern European ancestry from my 2011 test with 23&Me. My great-grandfather was from a small village in the Ukraine (which was part of Russia back then). The test showed my Ukrainian ancestors' genetic haplogroup originated in the Scandinavian regions thousands of years ago. They migrated down into Russia/Ukraine from that area. I'm not sure how common that is amongst the people of that area.

I've heard MyHeritageDNA is decent if you're looking for more detail on Russian heritage.