In 1884, Georges Seurat, known as George in the musical, is sketching studies for his famous painting, "A Sunday Afternoon on the Island of La Grande Jatte." He conjures up the island, a small suburban park, around him, and retains some control of his surroundings as he draws them. His longtime mistress, Dot, models for him, despite her frustrations at having to get up early on a Sunday. More regulars at the park begin to arrive: a quarrelsome Old Lady and her Nurse discuss how Paris is changing to accommodate a tower for the International Exposition, but the Nurse is more interested in a German coachman, Franz. The quiet of the park is interrupted by a group of rude bathers. George freezes them with a gesture, setting them as the subjects of his first painting, Bathers at Asnières. The setting abruptly changes to a gallery where the painting is on display. Jules (a more successful artist friend of George's) and his wife Yvonne think George's work has. Back on the island, Jules and Yvonne have a short discussion with George and depart. They take their coachman Franz with them, interrupting Franz's rendezvous with the Nurse. Dot, who has grown tired of standing still in the early morning sunlight, leaves the park mollified after George promises to take her to the Follies. George approaches the Old Lady, revealed to be his mother, and requests to draw her, but she bluntly refuses.
In George's studio he works on his painting obsessively while Dot prepares for their date and fantasizes about being a Follies girl. When George briefly stops painting to clean his brushes, he and Dot reflect on how fascinated they are by each other. Dot is ready to leave, but George chooses to continue painting instead, greatly upsetting her.
In the park, on a Sunday some time later, George sketches a disgruntled Boatman to the disapproval of an observing Jules. Dot enters on the arm of Louis, a baker. Two chatting shop girls, both named Celeste, notice Dot with a new man. When Jules and Yvonne's daughter Louise attempts to pet the Boatman's dog, he shouts at her, then lashes out at George and storms off. George and Dot have an awkward, strained conversation as she works on the grammar book she is using to teach herself how to read and write. As Jules and Yvonne mock the unconventional nature of George's art, they discuss an initiative to have his work included in the next group show, which they both protest. George sketches two dogs while whimsically trying to imagine the world from their perspective, describing their relief to be free of their routines on Sunday. As the day goes on, George quietly sketches denizens of the park: The two Celestes try to attract the attention of a pair of Soldiers, fighting over which will get the more handsome of the two; The Nurse hides from the Old Lady and attempts to attract Franz's attention; a Franz and his wife Frieda argue with Louise and each other; a pair of wealthy American tourists pass by, hating everything about Paris but the pastries, and plan to return home with a baker in tow; Jules returns to further lecture George on his shortcomings as an artist, receiving in response an invitation to see his new painting; the Boatman reappears to rebuke the condescending attitude of artists. Dot sees George, but he slips away before she can speak to him, and in retaliation she describes her satisfying new life with Louis. She clearly misses and loves George, but Louis loves, respects and needs her in a way George cannot, and she has made her choice.
As the park empties for the evening, George returns. He misses Dot and laments that his art has alienated him from those important to him, but resigns himself to the likelihood that creative fulfillment may always take precedence, for him, over personal happiness.
Time has passed, and a heavily pregnant Dot visits George's studio. She asks for a painting George made of her, but he refuses. Jules and Yvonne come to the studio to see George's nearly-finished painting. While Jules goes with George to see the painting, Yvonne and Dot hold a wary conversation. Once they realize they have both felt neglected at the hands of an artist, their mutual dislike fades and they discuss the difficulties of trying to maintain a romantic relationship with an artist. Meanwhile, Jules is puzzled by George's new technique, and concerned that George's obsession with his work is alienating him from his fellow artists and collectors alike. He refuses to support the work. Jules and Yvonne leave, and George, having forgotten Dot was there, goes back to work. Dot reveals the real reason for her visit: despite the obvious fact that her unborn child was fathered by George, she and Louis are getting married and leaving for America. He angrily retreats behind his canvas, and she begs him to react, in some way, to her news. They argue bitterly about their failed relationship, and Dot concludes sadly that while George may be capable of self-fulfilment, she is not and they must part.
In the park the Old Lady finally agrees to sit for George, losing herself in fond memories of his childhood that George repeatedly points out as false. She bemoans the changing skyline of Paris, and he encourages to see the beauty in the world as it is, rather than how it has been. The American Tourists arrive with Louis and Dot, who holds her newborn daughter, Marie. George refuses to acknowledge her, or his child, able to offer only a feeble apology as Dot departs sadly.
The park grows noisy: the Celestes and the Soldier argue over their respective break-ups while Jules and Frieda sneak away to have a clandestine affair in the park. Louise informs Yvonne of her father's infidelity and a fight breaks out between Jules, Yvonne, Franz, and Frieda. While this conflict develops the Celestes and the Soldier squabble noisily, and soon all the park-goers are fighting furiously, until the Old Lady shouts, "Remember, George!", and he stops them all with a gesture. George takes control of the subjects of his painting, who sing in beautific harmony as he transforms them into the final tableau of his finished painting.
In the tableau the characters complain about being stuck in the painting. The characters deliver short eulogies for George, who died suddenly at 31.
The action fast-forwards a century later to 1984. George and Dot's great-grandson, who is also an artist named George, is at a museum unveiling his latest work: a light machine called "Chromolume #7", an artistic reflection on Seurat's painting. George presents the work, grounding its connection to the painting by inviting his 98-year-old grandmother, Marie, to help him present the work. Marie shares her family history, describing how her mother, Dot, informed her on her deathbed that she was the daughter of the famous painter. George is reluctant to believe in that particular bit of family lore, but Marie insists that the notes in Dot's grammar book, which mention George, contain proof. After a brief technical failure, the Chromolume is unveiled.
At the reception, various patrons and curators congratulate George on his work while George flits between them, commenting about the difficulties of producing modern art. Like his great-grandfather, he conjures his surroundings, allowing himself to hold multiple conversations at once. The only voice he finds he cannot ignore is that of an art critic who advises him that he is repeating himself and wasting his gifts. After the museum's patrons have left for dinner, Marie speaks to her mother's image in the painting, worrying about George. When he arrives to take her home, she tells him about her mother, attempting to pass on a message about the legacy we leave behind. She dozes off and George, alone with the painting, realizes he is lacking connection.
Weeks later, Marie has died and George has been invited by the French government to do a presentation of the Chromolume on the island where the painting was made. On the island, George reveals to his friend Dennis that he has turned down his next commission. Feeling adrift and unsure, George reads from a book he inherited from his grandmother – the same book Dot used to learn to read – and ponders the similarities between himself and his great-grandfather. A vision of Dot appears and greets George, who she addresses as if he was the George she knew. He confides his doubts to her and she tells him to stop worrying about whether his choices are the right ones and simply make them. George finds some words written in the back of the book – the words George often muttered while he worked. As George reads them aloud the characters from the painting fill the stage and recreate their tableau. As they leave and the stage resembles a blank canvas, George reads: "White: a blank page or canvas. His favorite – so many possibilities."