NEW YORK — “Rent” alum Anthony Rapp is giving fans of the iconic musical — about friends contending with life amid the AIDS epidemic in early 1990s New York City — a peek behind the curtain. “Without You,” based off Rapp’s one-man musical and memoir of the same name, will have its opening night at New World Stages on Jan. 25, 2023, marking exactly 27 years since the first public performance of “Rent” at New York Theatre Workshop. The limited run, whose public performances kick off Jan. 14, will take its final bow on April 30. “In 1994, Anthony Rapp was 22, out of money and working at a Starbuc…