Aeroflot has an interesting low fare opportunity from Los Angeles to Vilnius, Lithuania VNO for $676 round trip. The unique aspect of this ticket is the possibility to turn a long layover into a full 23.5 hour day in Moscow from 1:00pm arrival at SVO to noon departure the following day from Moscow SVO. You can probably get to Vilnius for an even lower price via Stockholm, but the long 6-hour layover in Moscow SVO on the way to Vilnius would not be bad if you have airport lounge access.
There seems to be a general sale for Aeroflot fares from LAX to several airports around Europe via Moscow SVO. This SkyTeam partner airline periodically has some of the best sales from Los Angeles to Europe.
Aeroflot Los Angeles LAX – Moscow SVO – Vilnius VNO
$675.56 round trip Sunday October 23 – Sunday October 30
Personally, I don’t want to be bothered with visa paperwork and fees for a 24 hour layover. I have no knowledge of the visa process for an overnight in transit ticket in Mocow, but I’d look into this if I wanted to visit Moscow for a day for the same ticket price as a trip to Vilnius, Lithuania.