You might want to spend some time browsing the exhibits at Metro Museum, New Tretyakov Gallery - Museum of Modern Art, or Pushkin House Museum on Arbat. Novodevichy Convent, Shukhov Tower, and Cathedral of Christ the Savior are some of the notable landmarks to see in the area. You can watch performances at Festa Di Voce Music Theater, Glas Russian Spiritual Theatre, and Moscow International House of Music if you're interested in local theater.