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, Arbat Street, and A. N. Scriabin House Museum are some of the notable landmarks to see in the area. You can watch performances at Bolshoi Theatre, Maly Theatre, and Tik Tak Theater if you're interested in local theater.