It’s the hoariest of musical theater plots: A young woman flees a small Midwestern town for the bright lights of New York, singing and dancing her way from innocence to experience. In this case, the woman — or girl, in the parlance of the mid-1960s — wants to be a photographer, and her subject will turn out to be America in the throes of a cultural revolution.

The vehicle, a jukebox musical on the model of Mamma Mia!, is A Sign of the Times, presented by the Delaware Theatre Company in a regional premiere with Broadway aspirations. The show pairs songs from the Petula Clark catalog (including “Downtown,” “Don’t Sleep in the Subway,” and the title number) with Janis Ian’s haunting “Society’s Child,” the Nancy Sinatra hit “These Boots are Made for Walking,” and the Monkees’ “Last Train to Clarksville,” among others.

Part of the fun is seeing how these random songs mesh — or fail to — with the frothy book by the Emmy-winning comedy writer and actor Bruce Vilanch (based on a story by Richard J. Robin). But the result needs to be sharper and funnier. Though Vilanch name-drops the causes of the time, from civil rights and the Vietnam War to the rising consciousness of women, he never goes very deep, or tells us — at least the baby boomers among us — anything we don’t already know.

Director Gabriel Barre, whose approach can be frenetic at times, oversees a cast with Broadway credentials and polish. Chilina Kennedy (Carole King in Beautiful) is a likable Cindy who delivers powerhouse performances of the feminist anthem “You Don’t Own Me” and the rousing “Downtown.” As Brian, the tippling advertising man who becomes Cindy’s own personal Don Draper, Ryan Silverman oozes first charm, then sleaze. (Too bad Mad Men’s Matthew Weiner wasn’t on hand to write his lines.) Drew Seeley’s Matt, Cindy’s beau from Centerville, Ohio, is authentically retro as the boy (more or less) next door who wants his little woman at home.

But the real hot center of the musical is Crystal Lucas-Perry’s Tanya, who is Cindy’s New York roommate. Tanya profits from her status as an in-demand “token” black woman — one of Vilanch’s wittier conceits — and stumbles into an interracial romance with the nonviolent, injury-prone rabble-rouser Dennis (Stephen Grant Douglas). She belts out “Rescue Me,” infuses “Society’s Child” with melancholy, and is simply an electric presence.

The electricity reverberates across the stage in choreographer JoAnn M. Hunter’s ensemble dances, which quote the Frug and other crazes of the era. Jen Caprio’s vibrant costumes — floral minidresses, peasant-style blouses and skirts, dashikis, and Cindy’s patchwork suede skirt — glow in Ken Billington and Jason Kantrowitz’s psychedelic lighting.

Paul Tate dePoo III’s sets morph from a realistic Midwestern kitchen to the more loosely modeled streets, clubs, offices, and apartments of New York. Projections by 59 Productions add color and atmosphere, capture Cindy’s street photography, and, finally, convey us through the decades to (almost) the present moment.

Highlighting the ubiquity of sexual harassment, pay discrimination, and other forms of gender inequality in the 1960s, A Sign of the Times lays claim to contemporary relevance. But it functions mostly as an exercise in nostalgia, easy to digest and easy to forget.

A Sign of the Times. Through Dec. 23 by the Delaware Theatre Company, 200 Water St., Wilmington, Del. Tickets: $25-$72. Information: 302-594-1100, delawaretheatre.org.