I was sitting at the George Sherman Union the other day when an older gentleman approached me and asked about the sticker of actress Lauren Bacall pasted on the back of my laptop. After bonding over our shared love of Jean Arthur comedies from the 1930s, the man posed a question: How can we get more kids your age to watch old movies?

Following famous journalistic films like “Spotlight” and “Citizen Kane,” director Steven Spielberg, actress Meryl Streep and actor Tom Hanks all come together for the first time in “The Post,”...