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. Shukhov Tower, Novodevichy Convent, and Cathedral of Christ the Savior are monuments to see when you're exploring the area around Gagarinsky. 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.