You might want to spend some time browsing the exhibits at Museum of History of Moscow, New Tretyakov Gallery - Museum of Modern Art, or Pushkin House Museum on Arbat. While you're exploring, swing by Cathedral of Christ the Savior, Arbat Street, and The Cherry Orchard Theater to learn a bit about the area. You can watch performances at Anton Chehov's Theater, Theatre on Malaya Bronnaya, and Tik Tak Theater if you're interested in local theater.