Here’s the thing about Hugh Jackman. His talent merits a spotlight, he looks very good (still) in a spotlight and, unlike the vast majority of his peers, he can absolutely be relied upon to know the name of the spotlight operator.

Perhaps unsurprisingly, in his new concert residency at Radio City Music Hall—titled “From New York, With Love” and totaling 24 performances stretched across weekends through Oct. 4—Mr. Jackman leans into the cinematic half of his career,