The main streets of Shin-Okubo — Tokyo’s Koreatown — are lined with smoky barbecue restaurants and overlit cosmetics emporiums. Staircases lead down to basement music venues and up to hidden drinking holes. Japanese once thronged the neighborhood, which is home to many ethnic Koreans and known for its fiery food and late nights. But in recent months, the crowds have thinned, replaced by anti-Korean protesters who have turned Shin-Okubo into a rough barometer of deteriorating Japan-Korea relations.