You might want to spend some time browsing the exhibits at Rumyantsev Mansion, C-189 Submarine Museum, or Erarta Museum and Galleries of Contemporary Art. Yusupov Palace, St. Petersburg Academy of Fine Arts, and St. Isaac's Cathedral are well-known local landmarks worth a visit. You can watch performances at Mariinsky Theatre, Tovstonogov Bolshoi Drama Theater, and Mikhailovsky Theatre if you're interested in local theater.