You might want to spend some time browsing the exhibits at Cruiser Aurora, Pushkin Flat-Museum, or Erarta Museum and Galleries of Contemporary Art. Peter and Paul Fortress, Spit of Vasilievsky Island, and Rostral Columns are well-known local landmarks worth a visit. You can watch performances at Alexandrinsky Theatre, Mariinsky Theatre, and Rimsky-Korsakov Conservatory if you're interested in local theater.