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