You might want to spend some time browsing the exhibits at Russian State Museum of the Arctic and Antarctic, Dostoyevsky Museum, or Faberge Museum. Some landmarks that you won't want to miss include Tauride Palace, Anichkov Palace, and Smolny Cathedral. You can check out the local talent at Oktyabrskiy Big Concert Hall, Leningrad Center, and Bolshoi Saint Petersburg State Circus.