You might want to spend some time browsing the exhibits at Pushkin Museum of Fine Arts, Museum of History of Moscow, or Pushkin House Museum on Arbat. Cathedral of Christ the Savior, Anton Chehov's Theater, and The Cherry Orchard Theater are some of the notable landmarks to see in the area. You can watch performances at Theatre on Malaya Bronnaya, Moscow Arts Theatre, and Chekhov Art Theater if you're interested in local theater.