Great places to have a lot of fun, and do a lot of sightseeing! Recommend you get in the habit of putting your wallet in your FRONT pocket. This way it will be tougher to lose it.
Must see places include the Kremlin and Red Square in Moscow, as well as the Hermitage (the Winter Palace) and the Summer Palace in St Petersburg. If you go to the Kremlin, check out the Armory. It has all of the crown jewels of the Romanoff Dynasty on display (sorry, no photos allowed). Photos aren't allowed of paintings in the Hermitage either (flashes ruin them), but the Throne room is impressive to see. If you like art, I highly recommend the Tretiakovsky Art Museum in Moscow. I also recommend the tour boats that take day tours of the canals in St Petersburg as it is a great way to view the architecture of the old city.
It might help to search around for a local guide who speaks English, as it can be difficult to impossible to communicate otherwise. The female guides are downright HOT too! If you don't, try to learn some russian, including the Cyrillic alphabet, as there are no translations of signs into Arabic lettering.
Security is tight in Moscow. Do not be surprised if a Soldier or Policeman walks up to you, salutes, and says "Papers". He is just asking to see your passport and visa, and should send you on your way with no questions asked.
Avoid inviting locals to your room. They will slip a Micky Finn in your drink and you will wake up the next morning missing your wallet, money, papers, and anything they consider valuable. If any Gypsy boys try begging money from you, I've found that yelling "Scram!" at them will send em on their way. They don't understand the word, but it scares em nonetheless.
Enjoy your trip! I wish I was going there before next year!