Viktoria, welcome to the forum. 

There is not single "Russian district" in Atlanta.  Even in areas where majority of the Russians live, it's unlikely that you will see or meet any of them on the street or have Russian neighbors.  That's why we have this website

Most Russians who move to Atlanta find location convenient to work, good schools, and proximity to the Perimeter.  Any of the areas that KGBMen mentioned are good.  Avoid moving too far away from the city, if you can afford it.