(covers information from several alternate timelines)
A utopia was a world in which everything and everyone was supposed to work in perfect harmony. What constituted a utopia was subjective, as one person's idea of a perfect world might be predicated on abusing, exploiting, or even eradicating another.
In 2259, Pelia described the New World Economy as a "no money, socialist utopia". (SNW: "Tomorrow and Tomorrow and Tomorrow")
In 2268, James T. Kirk described Platonius in his captain's log as a utopia patterned after Ancient Greece. Philana later explained to the crew that as the products of Sahndara's eugenics program, she and her 37 fellow Platonians were perfect for their utopia. Parmen would characterize their society as a utopian brotherhood.
Kirk noted that their utopia was "one of the best-kept secrets in the galaxy". Upon witnessing their cruel manipulations of his crew, Kirk questioned, "Is this your utopia, your grand vision of the future?" Later, Spock, upon learning that the secret of their powers was kironide surmised it was why their utopia was a secret. (TOS: "Plato's Stepchildren")
Bele criticized Lokai's desire to free his people as having "asked for utopia in a day", an impossible task in his opinion. Lokai then retorted that "Genocide for my people is the plan for your utopia." (TOS: "Let That Be Your Last Battlefield")
In 2365, upon learning that the Mariposans were descendants of Neo-Transcendentalists, whose philosophy called for a simpler life, Jean-Luc Picard questioned why these utopians had a lot of technological cargo on their ship. (TNG: "Up The Long Ladder")
Around 3052, Jonathan Archer tried to sympathize with Daniels that his future, which Archer called Daniels' "little utopia", had vanished, but insisted he needed more information. (ENT: "Shockwave, Part II")