You might want to spend some time browsing the exhibits at Rerikh Museum, Pushkin Museum of Fine Arts, or Pushkin House Museum on Arbat. Cathedral of Christ the Savior, Arbat Street, and Armoury Chamber 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.