The same applies to St Petersburg as to any other megapolis in the world: don't deal drugs on the streets, stay out of gang warfare, do not wear your guns visibly and never hit a policeman. If you follow the basic rules what might also apply to your city of origin there could be no problems.
While I was in Russia I saw an incredible amount of accidents. For my liking, the Russian driving is a bit reckless. This picture was taken in Nevsky Prospect where an accident had just happened.