You might want to spend some time browsing the exhibits at Russian State Museum of the Arctic and Antarctic, Dostoyevsky Museum, or Faberge Museum. Beloselsky-Belozersky Palace, Anichkov Palace, and Tauride Palace are landmarks that you won't want to miss. You can watch performances at Oktyabrskiy Big Concert Hall, Bolshoi Saint Petersburg State Circus, and Alexandrinsky Theatre if you're interested in local theater.