You might want to spend some time browsing the exhibits at New Tretyakov Gallery - Museum of Modern Art, Pushkin House Museum on Arbat, or Memorial Apartment of Andrei Bely. 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 Theatre on Malaya Bronnaya, Moscow Arts Theatre, and Andrey Shchukin Theater Arts Workshop if you're interested in local theater.