Take plenty of US cash in small bills. They don't want rubles and will give you change in rubles if they can to preserve their supply of US dollars. I made the mistake of taking very little cash thinking I could use travelers checks. The hotel would only convert them into rubles. Lucky for me, people were generous enough to loan me some cash until we got out of Russia.
Theft is a very big problem in Moscow.
Seveal people had their bags cut open and valuables removed - before they were delivered by baggage people. Carry your handbag in front of you as well as over your shoulder. Take as few valuables as possible. Always keep your passport and money under lock and key within your room. Better yet, take it with you always.