You'll want to browse the collections at Glinka National Museum Consortium of Musical Culture, Pushkin House Museum on Arbat, and Moscow Museum of Modern Art. While you're exploring, swing by Lenkom Theatre, Yeliseyev Grocery Store, and Arbat Street to learn a bit about the area. You can watch performances at Tik Tak Theater, Tchaikovsky Concert Hall, and Stanislavski and Nemirovich-Danchenko Moscow Academic Music Theatre if you're interested in local theater.