When will “Good Morning America” anchor Josh Elliott and WABC-TV’s beautiful Liz Cho finally go public as a couple? Reliable sources tell us that handsome morning anchor Elliott was spotted leaving Cho’s Upper West Side apartment just after lunchtime on Thursday, with one spy telling us, “It seems he heads to her apartment after he’s finished ‘GMA.’ ” Page Six revealed last September that the anchors had started dating after Cho separated from her husband, Evan Gottlieb. An ABC source added, “Everybody at the network knows they are seeing each other, but still they are trying to remain discreet.” While he has been on many dates with Cho, friends say Elliott remains a “man about town” and feels the gossip about his busy love life is being planted by enemies to derail his career. An ABC rep declined to comment.