Since the answers so far have only covered mainstream fictional worlds, I must now put on my hipster glasses. There.
In answer to the question, while Star Trek wouldn’t be too bad, for me, the obvious answer would easily be The Culture, the eponymous post-scarcity interstellar civilization described by Iain M. Banks.
What is the Culture?
“Hippies. With nukes.”
— Iain M Banks
Occupying roughly the intersection point between society, movement, heritage and IRC chat room, the Culture is a hegemonic, though remarkably peaceful, force in the known galaxy. It’s an anarchist, transhumanist, posthuman, space-faring utopia (although like any utopia it does have its significant flaws). As such, it is a consensus-based society which is largely space-based. As Wikipedia puts it,
… the Culture is composed of several inter-bred humanoid species, as well as artificially intelligent sentient machines, with intelligences ranging from human-equivalent drones, to hyper-intelligent Minds. The Culture's economy is maintained automatically by its non-sentient machines, with high-level work entrusted to the Minds' subroutines, which allows its humanoid and drone citizens to indulge their passions, romances, hobbies, or other activities, without servitude.
The Minds are generally housed in great vessels or habitats, and their vast abilities (intellectual and material) afford them the defacto status of elders. Although there is a consensus based, thoroughly democratic governance, and although the Minds themselves abhor exploitation, compulsion and servitude, it is ultimately difficult for mere biological beings to intellectually compete with an entity able to simulate entire universes in real-time.
Humans in the Culture, then, are able to do pretty much whatever they want because, although their aggregate contribution is certainly valued, it isn't necessary in any absolute sense. They are left to pursue their own interests and, if they so wish, to tag along on a Culture vessel, a bit like a weird cross between a houseguest, a hitchhiker, a backpacker and a housepet.
Why would you want to live there (when you could live in the Federation of Star Trek?)
Because the average Culture citizen leads a life that makes life in the Federation of Star Trek look like abject poverty.
Any Culture citizen can expect a lifespan of at least four centuries (presumably infinite, should they choose to upload themselves). Their engineered bodies are capable of consciously controlling their own metabolism, moods, and hormone cycles, with the option of complete or partial sex change in a matter of weeks. They have full Internet-equivalent access built into the brain via the neural lace (covering all the senses if desired), which also provides enhanced memory and recall, a heads-up display, a machine interface, and temporary mental speed-up (combined with the ability to gland various stimulants, this can briefly allow them to plan and react as if normal humans were standing still).
The Culture has no need of money. No, not in the way they say Star Trek works, with its replicator rations and its scarce Latinum; I’m talking actual lack of money. The effectively limitless industry of a post-scarcity society means that any conceivable material needs are taken care of automatically. If a Culture citizen wants to own a planetoid or a mile-long star cruiser (although the impulse to do so would seem a bit needy to a Culture citizen), that’s not really an issue. If they wanted to recreate fractal cityscapes across the surface of a moon, they can do so. Restrictions only come in when what the person wants is clearly inimical to other intelligences, or when they don’t find anyone else willing to collaborate on whatever project they come up with. In the case when one’s wishes bump up against the well-being of others, there are various forms of counterfeit reality — the most radical meaning that you’ll be living out your life completely immersed in a fantasy world catering to your evil whims.
So yes, even life-long incarceration by the Culture might be considered paradise in your typical SF universe.
Sounds boring. Wouldn’t you want to go on an adventure?
If I lived in the Culture? Heck no. They wouldn’t really need me to do so, and so I wouldn’t feel the urge to possibly get into harm’s way.
Sure, there would probably be people willing to risk their lives in service of Contact or Special Circumstances, and good on them, but if I wanted the carefully-metered illusion of danger, I could do that just by spending my sleeping periods participating in shared dreamspace playing the part of an action hero. Or extreme sports with a backed-up mindstate. Or whatever it is that Culture citizens would dream up when those activities get stale.
I’m a simple soul. I don’t care much for exploration if that means I’m forced to spend said exploration in the void between star systems dressed only in a unitard, living in perpetual fear of someone sneezing and accidentally causing the warp core to detonate. I’m not knocking the choice, but it’s not my cup of tea.
Me, I’m choosing a world of full-immersion VR scenarios where I can literally live out my dreams in whatever manner I choose. A world in which I could study my favorite subjects under a superhumanly gifted tutor. A world where I spend my leisure periods attending parties, orgies, moon-sized libraries or any games I could think up (or possibly all of the above at the same time), all while wearing the body of my choice.
For four centuries in my own body, or eternity.
Not too shabby, right?