I didn't feel less safe in Moscow or St. Petersburg then in any large American city. Just be careful, keep your wallet in your front pocket when in a crowd, keep pocketbook in front of you. We did feel like we were 'being sized up' when coming out of some of the metro stations. We also felt one time that we were being followed. We stayed in public places and they stopped 'following' us. We had a great time!
Scott