We are going to travel to Russia (St Petersburg and Moscow). Is there any red light district (or something like that) in these cities? Where are these places?
Are they safe for tourists?
No, there are no such districts in either Moscow or St. Petersburg as of 2016. Prostitution is illegal in Russia and locations which become too well-known to the public are frequently raided and shut-down.
Obviously prostitution still exists, but it's not centered in any particular street or district. There are many websites online dedicated to reviews of such establishments, so you can try your luck on the Internet.
As for safety: unless you speak Russian without an accent, I wouldn't risk it. While those two cities can be generally safe, putting yourself in contact with the underground sex trade is a risky endeavor for foreigners.