You might want to spend some time browsing the exhibits at Pushkin Museum of Fine Arts, Pushkin House Museum on Arbat, or New Tretyakov Gallery - Museum of Modern Art. 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 Bolshoi Theatre if you're interested in local theater.