You might want to spend some time browsing the exhibits at Metro Museum, New Tretyakov Gallery - Museum of Modern Art, or I.S. Turgenev Museum. Novodevichy Convent, Novodevichy Cemetery, and Pushkin House Museum on Arbat are some of the notable landmarks to see in the area. You can watch performances at Great Moscow Circus, Moscow International House of Music, and The Man Theater if you're interested in local theater.