While racism does exist in Russia, to be honest I think you are really going to have to go out of your way to find Moscow suburbs where you might encounter serious violence and any marauding gangs of skinheads.
The city is huge, if you are going as tourist you are highly unlikely to venture beyond the city centre where ethnic diversity is common. In the times I lived there none of my 'dark skinned' friends or colleagues ever experience violence (in fact the only person I know who did was a white Scotsman!).
Yes, bad things can happen - but they do in most big cities; employ common sense and you ought to be fine.
This previous thread might also be of interest - someone who was convinced Russia would be horrible but in the end had a great time!:
http://www.flyertalk.com/forum/russi...-russia-3.html