Sure, I think they can be constructed around a singular person, and I think
@Quickleaf hit on some aspects how these places come to be. They are essentially wish fulfillment, but they've gone to far. The individual got their wish, but in some way realized it wasn't what they really wanted after all.
The Land of Never. Tom was a child who never wanted to grow up, never wanted the responsibilities of adulthood and wanted to live a life of adventure. A powerful fey gave Tom his wish, all for the mere cost of his shadow. Tom willingly agreed and was swept away to a mythical island of mermaids, pixies and pirates. Tom was most intrigued by the pirate king, who led a merry band of scalawags. He tried to mimic the pirate king, gathering to him a group of other lost children to create a gang of his own to counter the pirate king's band. But he's just a kid, and no one really takes him seriously. Sometimes, he wonders - just wonders, what it would like to be grow up and be a responsible adult...
The Thousand Acre Woods. Kristopher was a lonely, sickly child with no friends, until one day, when talking to his stuffed animal friends, it responded. It offered Kristopher friendship if he would come to the nearby forest and bring all of his stuffed animals with him. Kristopher happily agreed, and with an armful of his favorite stuffed animals, made his way into the deep woods. There, in a perfect glade, his friends awoke, and they talked and played until Kristopher realized he was hungry. But when Kristopher attempted to return home, he found every path led back into the glade. His new friends happily took him back to their home, fed him and put him to bed in the coziest bed he'd ever slept in, but sometimes he gets homesick, but can never quite find his way home...
Where Wild Things Live. Maxie was a precocious child, who loved to stomp around the house in her fearsome tiger pajamas. One night though, she broke her mother's favorite vase as she chased the household dog. Maxie was sent to her room, where she stewed over her silly punishment. After an hour or so, a strange, kindly monstrous being with great yellow eyes appeared at her window and beckoned to her. "Come with me," it kindly told her, "and no one will ever tell you what to do again." Maxie didn't look back as she climbed out the window and onto the creature's back, finding it floating on a cloud. Like a great boat, the white cloud whisked both through the night sky, until it disappated over a jungle-covered island in the pearly blue sea. Maxie fell with a scream, but her fall was broken by the huge leaves of the monstrous jungle, depositing her softly to the jungle's floor. When she finally stood back up, she found herself in a ring of curious, monstrous creatures who bowed before her as queen. Jubilant and unafraid, Maxie took on the title and commanded her new follows on a great rumpus through the spooky jungle. She rolicks there still, sometimes wondering if her mother is still mad at her...
Beyond the Magic Mirror. At the foot of the Vale of the Mage lies a curious cave with a single chamber. At the back of this chamber stands a towering silvered mirror that casts the reflections of everything but the living. They say that the Mage's daughter, Alicia, spurned her father's teachings of magic and disappeared through the mirror long ago, but few know its location and fewer have returned from its reflection. Those that have returned half-mad, speaking of talking flowers, soldiers made of cards and a curious hatter who is quite insane...
The First Land. It has been passed from family member to family member for generations, yet it is spoken of with awe. To the uninitiated, it appears as a single teakwood standing wardrobe closet, filled with moth-eaten otter furs. But with the doors closed behind them, those within the closet find that the furs give way to fir trees, and eventually to a fantastic realm of talking animals and mythical creatures. Ruling over this land is the great lion Nobanion, who looks over the descendants of a child he befriended long ago, helping those descendants in times of their greatest need.
I could go on, but I think you get the gist...
(Oh, and I think Disney's Aladdin would make a superb Realm of Delight too - who doesn't want to be prince ... until they can't get away from the responsibilities...)