What denomination and condition of USD bills ($20, $50, $100 etc.) are most readily convertible in Moscow and is it banks or money changers that offer better exchange rates?
Ideally, bring crisp, new, undamaged $50 and $100 bills. You can find exchange rates on various web sites, e.g. here's a map of Moscow showing rates at various locations: http://4map.ru/ (you need to enter all your parameters on the left side, the currency pair and the amount, and then click the grey button to show the rates on the map).