The universe of the Cthulhu Mythos of H.P. Lovecraft et al.
I’d love to live in Charles de Lint’s Newford. First thing I’d do would be to go out for drinks with the (shapeshifting) crow girls. After reading several books and volumes of stories set there, the residents and their storylines feel practically real already.
It’s been thirty years since I’ve read it, but Ringworld (Larry Niven) would be an awesome place to live.
I would love to visit Newford for a Drink and some Celtic Folk music, but I would want the “Prancing Pony” to the place where everyone knows my name. 
Jim
In most sci-fi universes, I assume I’d be the same regular person I am in this universe, so which universe seems to offer the most interesting lifestyle for a regular guy?
Star Wars. Those people seem to have the coolest stuff, and you don’t have to be some galactic hero to experience it. With a little brains, talent & hard work, it doesn’t seem too unrealistic to find yourself a job that could take you all around the galaxy.
Star Trek is a close second, but it seems like once you get used to having teleporters & food replicators, it’d be kinda boring.
Dune? I’d just be some lowly subject on some planet where as likely as not, I’m being oppressed.
Ringworld? I’d spend my whole life never even knowing I was on a Ringworld.
Marvel/DC comics? I’d be who am now, only reading about super heros in the paper. “Oh, the Earth almost got destroyed again today, but some dude saved it.”
Does anyone else know Callahan’s? (Spider Robinson’s famous bar)
This would be a great place for Dopers to gather and debate and exchange stories and ideas. If we need to be regular people, at least we could have a great place to hang out.
Jim
I’ve got to vote for the Firefly 'verse. I certainly feel like I can visualize it and immerse myself in it than any other SF universe. In just a few short episodes we learned an awful lot about it. Their history, their major war, the government, life on the borders, all levels of their technology…
Second choice for me would be Heinlein’s Future History. Just 'cause I like the people in it so much.
Anybody for Poul Anderson’s Polesotechnic league universe?
Sure I do. 
Thanks for the reminder. I need to get back to those stories.
Pretty much anyone who enjoys de Lint and Callahan’s is Good People, as far as I’m concerned.
Callahan’s Law: “Shared pain is lessened; shared joy, increased”
– Spider Robinson
I’d like to put in a word for Jack McDevitt’s worlds described in Chindi and Omega. Not so much fabulous tech stuff (although there’s a deal of that) but two things: sometimes the good people win against the bureaucrats, and everything feels very real the way he writes it.
This is in spite of the Stephen King blurb they keep insisting on putting on the front covers. 
Also love Callahan’s.
Have to second Discworld, Culture and Middleearth.
My adds (OP didn’t ask if we’d like to live there, just if you like it, and why):
The Valley of the Na, from Ursula LeGuin’s Always Coming Home - LeGuin’s very good at writing “real Utopian” worlds (see also Banks’ Culture), and this is her best one. It’s a culture I can admire and want to visit, which given that it’s riven through with un-Dibbley spirituality, is quite an achievement. It’s a quasi-utopia that doesn’t require the inhabitants to be saints, with a nice mix of Amerindian and Zen beliefs. One of my all-time fave SF books.
Bas Lag, China Mieville’s works. I certainly wouldn’t want to live there, but I like the fact that for all the elements of the fantastic, it’s not another Middle Ages feaudal clone world. People are realistic, and politics is diverse, not a variant on “to play the King” as seen in countless other SF books.
That’s an excellent standard, and the place you want to live is in Banks’ Culture universe, where billions of ordinary citizens command resources that would make Bill Gates’ jaw drop in envy.
Another vote for Callahan’s Place and Known Space/ Ringworld. Another would be Andre Norton’s Witch World and Free Traders universes. Lots of history and sense of wonder in both.
One of:
Peter F Hamilton’s ‘Confederation’ universe (‘Night’s Dawn’ trilogy and ‘A Second Chance at Eden’)
Discworld - of course.
Known Space
And I’d go to Vermillion Sands (Ballard) for my holidays.
The Clangers’ Universe***** obviously.
Discworld, goes without saying. Though I want to be a wizard, not some peasant in Sto lat.
The world of the Difference Engine (Gibson/Sterling) A meritocracy of sorts.
*****Which might, in fact, be our own, they are occasionally visited by astronauts and human built space probes.
I’d love to visit David Brin’s Uplift Universe. It wouldn’t be a very user-friendly place but it is filled with amazing species and wonders. Imagine playing a part in the Uplift of another species to sentience or trying to solve the mystery of the origins of intelligent life.
Another vote for Discworld. Ankh-Morpork would be a wonderful place to spend some time. To but something onna stick from CMOT Dibbler would be an adventure in itself. I imagine myself as being an American version of Twoflower, wandering aroind filled with wonder while not having a clue to what was going on around me.
Another vote for Amber but only if I had the power to walk between universes. To walk until you reach the place of your desires, what more would a person need?
I’d also like to visit Adrilanka, with the proviso that I would have the life span of one of the Human rulers. To be limited to the 70 or 80 years of an easterner would be cruel.
I’d also like to visit Chalker’s Well World, provided I’d be able to travel from hex to hex and change my species and sex whenever I wanted to.
I wouldn’t like to live there either, but I would like to visit Perdido Street Station. It sounds like an impressive building.
Being on Edgar Rice Burroughs’ version of Mars (Barsoom)would be my choice, as long as I was John Carter of course and with Dejah Thoris.
Not unless I had a lot of power backing me up, given the attitude the Draegareans (sp) have towards Easterners. The Sword of the Rivan King sounds about right.
Another good one.
I think my top five, in no particular order, would be:
Tolkien’s Middle Earth (It’s just the gold standard)
DC Universe BEFORE the Crisis on Infinite Earths (it was a lot more fun then)
Firefly (whatever problems it has it more than makes up for with cool)
Foundation (again, what’s not to love)
Myth (by Asprin) because aparently no matter how powerful someone is, they are fairly easily duped and that could just be fun.
I got the distinct impression from the OP that the topic is not what universe you’d like to visit, but what universes do you find cool.
I may like Tim Powers’ creations, but I sure as hell wouldn’t want to be a character in one of his nooks. His heroes always end up completely thrashed.
I’d like to add Harry Potter to the list. I love the idea of a secret world of witches and warlocks right under our noses.
I must mention Discworld first, of course.
But actually Middle Earth may be my favorite.
Other faves:
Asimov’s Robot and Foundation universes.
Niven’s Lèshy Circuit and Magic universes.
Bank’s Culture
Aspirin’s Multiverse with Skeeve and Aahz
Moving on to TV/Movies …
The Babylon 5 universe
The Firefly 'verse