You might want to spend some time browsing the exhibits at Cruiser Aurora, LabyrinthUm, or Stieglitz Museum. Peter and Paul Fortress, Strelka, and State Hermitage Museum are monuments to see when you're exploring the area around State Museum of the Political History of Russia. You can watch performances at Alexandrinsky Theatre, Oktyabrskiy Big Concert Hall, and Mariinsky Theatre if you're interested in local theater.