On a chilly Thursday night in late January, four weeks from his last show as host of “Late Night,” Conan O’Brien was strumming a guitar behind his beat-up desk in his cluttered office at Rockefeller Center, figuring out how to say goodbye. After 16 years and 2,725 shows, O’Brien would be moving, along with almost all his staff, to Universal City in California to take over “The Tonight Show.”