The post-post-post apocalyptic Britain that Russell Hoban created in Riddley Walker
This is a favourite fictional culture in that it’s interesting, not so much in that I’d like to live in it.
I’ve always wanted to live in the world shown in Final Fantasy 7. Magic, steam punk devices, ninjas, and bigass swords. I want my own materia!
I want to live in Dante’s Cove. Everyone is under 30 (except for the immortal witches), everyone is wicked hot (including the immortal witches), everyone gets laid at the drop of a hat and I could kill people by looking at them.
This will come as no surprise but I would pick Aman as a Noldorian. Immortality, virtual freedom from disease and hopefully a chance to work with Aulë or at least his senior assistants. Of course I would want a chance to sail with the Teleri.
Jim
“May you live in interesting times.” 
That’s one way to answer the OP. If you want to know what fictional culture would be my favorite to actually live in, my answer is: the valley of the Kesh people from Ursula K. Le Guin’s Always Coming Home. It’s in Northern California many years in the future, a blend of rural living and in-tune-with-earth consciousness with subtle technological sophistication. (IIRC they have something like the Internet, for free, at a kiosk in each village.) Ordinary life there is good enough that in order to have sufficient conflict for a compelling story, the book’s protagonist had to leave the Valley and struggle to return.
For interesting it’s a toss-up between Banks’ Gas Giant Dweller culture (The Algebraist) and Mieville’s Bas Lag, especially New Crobuzon. Neither of them safe, nor would I want to live in either, but interesting to read about, yes.
The post-national tribal culture(s) of Neal Stephenson’s The Diamond Age – not something I’d want to live in, not something I hope ever exists IRL, but it is fascinating to watch how all those tribes coexist in parallel, with all their different ways and values, and form symbiotic economic relationships (e.g., the craftspeople of Dovetail and the hyper-professional Neo-Victorians), and work out their differences in the public sphere. Plus they’ve got nanotech!
I think I actually would like to live in the post-Green-Revolution culture of Kim Stanley Robinson’s Pacific Edge. (Callenbach’s Ecotopia – not so much; just a little bit too heavy, y’know?)
The post-eco-apocalyptic Neopagan culture of Yerba Buena (the San Francisco Bay Area) in Starhawk’s The Fifth Sacred Thing is also way cool. (Though I have serious doubts as to whether it would be practical to tear up the city’s streets and turn them into garden strips – they’re probably too polluted to grow anything, and then, even without cars, you still need streets, don’t you?)
Snow Crash.
When I saw the thread title I already knew I’d pick something from Middle-Earth, but I had to think a moment of which culture is my favorite. I’ve decided it’s definitely Hobbits. I can get behind honest work, a hot cuppa/evening in the pub, and 6 meals a day (when I can get them).
Merely The Diamond Age in embryo. (They’re set in the same fictional universe, separated by time – Y.T. from SC reappears as an elderly Neo-Victorian schoolmistress in TDA.)
Space-opera cultures are generally fun, if shallow – whether it’s Star Trek, Star Wars, Battlestar Galactica or the Lensman series – cultural values and assumptions are pretty much what you’re used to if you’re a middle-class white American, but the toys are so much cooler!
I think they would qualify as distinct cultures, given the massive changes during that time. The earlier world with its disequilibrium seemed more interesting.
1920’s chicago-as a member of the Bugs Moran (or Capone) gangs! Shootouts, bathtub gin, and big funerals!
So you would stay behind with Finarfin during the big exile?
I also want to be in Middle Earth, but I want to be a Noldor in Beleriand. For some reason I’m fascianted by Nargothrond, far more than Gondolin or Doriath. Sure, it would suck once the dragon comes, but not everyone died, right? And even then it’s just a little while in Mandos and on to Aman. What’s not to like?
I’m a little in love with Finrod Felagund, truth to tell. But I think that’s another thread entirely.
Ideally, I would stay behind, perfecting my craft and then go visiting Middle Earth in the third age or fourth age, maybe I could hitch a ride with Glorfindel or Gandalf. I would love to visit the Shire, Bree, Rivendell, the Ents, Lothlorien, Minas Tirith, the Glittering Caves and etc.
Jim
Not quite fictional…often fictionalized, though.
I want to live with the Vanderhoff-Sycamore-Kirby extended family in You Can’t Take It With You. “Behold the lilies of the field, they neither toil nor sow; yet God does all things needful yield that they may live and grow.”
minor hijack
Seeing Minas Anor, Minas Ithil and Osgiliath around the time of Isildur would be cool. I’d love to hang with Gil-Galad eventually as well. I also would like a pre-Balrog tour of Khazad-Dum.
I’m not asking for a lot, am I? heh.
/end hijack
The Loonie culture of Heinlein’s The Moon is a Harsh Mistress is fascinating, with its group marriages, line marriages, polyandry, and all the other ways that have been devised to deal with a massive gender imbalance under frontier conditions. (The apparent absence of prostitution is implausible, however – considering its prevalence in historical frontier societies with shortages of women.)