You'll want to browse the collections at Moscow Museum of Modern Art, State Historical Museum, and Nemirovich-Danchenko's Apartment Museum. Palace of the Romanov Boyars, Bolshoi Theatre, and Spasskaya Tower are well-known local landmarks worth a visit. You can watch performances at Moscow State Academic Chamber Music Theatre, Bogis Theatrical Agency, and Chekhov Art Theater if you're interested in local theater.