You might want to spend some time browsing the exhibits at New Tretyakov Gallery - Museum of Modern Art, Pushkin Museum of Fine Arts, or Armoury Chamber. Cathedral of Christ the Savior, Novodevichy Convent, and Pushkin House Museum on Arbat are well-known local landmarks worth a visit. You can check out the local talent at Moscow International House of Music, The Cherry Orchard Theater, and Taganka Theatre.