Again not sure where or price, but RWL Archives would have opinions from other travelers. I used a local Russian travel agency for Moscow and St. Petersburg, they did a great tour for me, so maybe check with them for you. They do tourist type tours, not the expensive dating tours for men wanting only to meet Russian Women. I arranged my other travel tickets myself. Yes, in many cases, but maybe not entirely fluent English.
Most Russian cities are safer than our cities here, especially for tourists doing tourist things.
The Mafia are not interested in tourists, but pickpockets around tourist areas are, and maybe muggers looking for someone alone. Just use common sense like you would here. Pack important or expensive items in your carry-on, they may be stolen from checked baggage. Carry a small pocket notebook to keep track of your trip, prices, gifts. Write down numbers or words to show others who do not speak English.