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