St Petersburg is the one port we always book P&O tours - IMHO it is the only sensible option especially if you have children with you. If you were to book with a Russian tour Company then do it well in advance as there are no ship side opportunities.
Very difficult as you have to get a visa - and for that you need a Russian sponsor. The dock is a fair distance from the town, it is a large city, some of the main attractions are outside of town, how do you plan to get around, do you speak the language......Suggest you use one of the registered russian tour companies [DenRus, Red October, Alla] - for them you do not need visas, you are with smaller groups and they can even tailor make tours for you.
First of all if you want to go ashore independently you need a Russian visa, which I believe is quite expensive. If you go on a ships tour, or on one of the Russian based tours, you don't need a visa. You just show your ticket to the immigration who let you in. The docking for large ships is in a very industrial dock area some way from the town.