You might want to spend some time browsing the exhibits at Gulag History Museum, Moscow Museum of Modern Art, or Nemirovich-Danchenko's Apartment Museum. Sights like Central Academic Theatre of the Russian Army, Lenkom Theatre, and Church of the Nativity of the Virgin in Putinki are landmarks to visit in the area. You can watch performances at Obraztsov Puppet Theatre, Hermitage Moscow Theater, and Sphere Moscow Drama Theater if you're interested in local theater.