In 1981, Billy Idol moved from London, where he’d had some success with his punk band Generation X, to Manhattan. He found a one-room West Village apartment, at One Sheridan Square, where his friend Ace lived. Recently, Idol, on the cusp of a big year—new album (“Dream Into It”), tour with Joan Jett (“It’s a Nice Day to … Tour Again!”), Rock and Roll Hall of Fame nomination, and documentary (“Billy Idol Should Be Dead”)—visited his old building. He emerged from a black S.U.V. in full Billy Idoliana: spiked blond hair, eyeliner, earrings, combat boots, leather jacket with zippers galore. Recalling his first New York summer, he made the doobie gesture, looking rascally. “Everybody kept their windows open,” he said, in a British accent with notes of Tufnel. “I could…