If you are going first time to Russia then definitely visit first Saint Petersburg. There is a lot to see and experience. Architecture is amazing and lots of beatiful cathedrals. There are really nice museums Hermitage (One of the biggest museums in the world) was mantionded already. Close to St. Petersburg or as locals call it "Piter", is huge summer palace wich is really amazing. One of the coolest ways to explore the city is by channels. Just jump into a boat, wchich is quite cheap and it will take you around the city.