Here is a romance that can’t happen, so why make a movie about it? In her early 20s, penniless Eleanor (Leighton Meester) desperately takes a job as live-in nanny for 12-year-old Reggie (Julian Shatkin), the only, lonely child of a wealthy family on Manhattan’s Upper West Side. We ought to hate the kid, a know-it-all prodigy who practices his cello in the family mansion’s conspicuously empty pool. (His parents are mostly absent; Debra Messing plays Reggie’s self-absorbed mother in a few early scenes.) But Reggie—we can’t help thinking of Richie Rich—is no brat. He’s a coddled vegan aesthete, encyclopedia pages pouring from his mouth. He plays chess on actual chessboards and reads old history books in hardcover, never on an iPad. (This preternaturally old soul was actually born after AOL.)

Gradually, on long walks through the park and one trip upstate, these two chaste lovers will share their secrets. Reggie has little in his past, of course, but for one family tragedy; yet we can feel secure that the Ivy League and a very large trust fund will ensure his future. Eleanor meanwhile comes from a poor, fractured Poughkeepsie family, yet there’s curiously little class resentment in Like Sunday. Reggie’s constantly bribing the servants and buying Eleanor expensive restaurant meals, which she never questions. Yet scenes with her needy/grating ex, effectively played by Green Day’s Billie Joe Armstrong, make clear this isn’t a fairy tale.

After her many seasons on Gossip Girl, Meester has a comfortable grace before the camera, though the script gives her little character to lift. Only when Eleanor finally confides her dashed dreams to Reggie do we realize (of both Meester and Eleanor) that Gosh, but this girl’s actually got some talent. Yet writer/director Frank Whaley never builds upon that potential. The same listless scenes play over and over (park, restaurant, cello, etc.), with odd editing lurches between them. Eleanor is shocked to discover Reggie can’t swim; the pool is empty; yet there’s no payoff. Most of the film is set during summer vacation, so the meandering might fit the rhythms of a grown boy’s distant memories of his first crush. Not Whaley’s memories—he came from Eleanor’s blue-collar, hard-drinking upstate wasteland, as recounted in his 1999 Joe the King. Eleanor feels like a refugee from that movie, unsure of her place in this one.

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LIKE SUNDAY, LIKE RAIN Opens Fri., March 27 at Sundance Cinemas. Rated R. 104 minutes.