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