It`s Absolutely safe in Russia. I’m from Moscow. Though some Russians might say they don’t like Americans, in reality they like foreigners! And honestly, I’ve met many people from overseas, and I can tell you, we have so many things in common with Americans. I wish everyone turned off TV and lived in peace and harmony… the only problem you will face in Russia is that most of us don’t speak English;) Visit Saint Petersburg, you will love it
Dont be afraid. It`s safe and civilized. I have not heard anything about big troubles with fans during The Word Cup. I will say that not long ago my friend went on a trip across Russia on the train and was completely satisfied with the journey. There is a special tour - rusrailtravel.ru/trans-siberian - Trans-Siberian Railway Tour from St. Petersburg to Beijing. Eighteen days on the road.
Russia is rather specific country, but it refers more to mentality, not safety in general. The prices for accomodation are really cheap, food and entertainment are very affordable, too. Moscow is rather expensive, but it is still cheaper comparing to the rest of Europe. I used travel services from this list travelsites.com/ and saved tons of money already.