Well, considering many of my favorite games feature worlds wherein the proverbial "shit" has hit the proverbial "fan", my choices are diminished.
Still, plenty left to pick from:
The world of Wipeout would be pretty damn sweet. Futuristic world that's a mix of Bladerunner and cyber-punk. A world where anti-grav technology reigns supreme and the most popular spectator sport is a ridiculous, over-the-top, incredibly fast, and ludicrously dangerous racing league. Could be interesting.
Same could be said of worlds like those of Deus Ex, Perfect Dark, etc. Places much like our world, only with far more advanced technology.
Another fun game world to live in would be that of Banjo Kazooie. Or, really, many of the classic adventure/platformer worlds. Donkey Kong Country, Conker's Bad Fur Day, Rachet and Clank, etc, etc.
'Course, at the same time, I imagine living in those worlds would be like being on a perpetual acid trip.
I could probably go on and on, but really, I think I'm torn between two picks. Mechwarrior and Torchlight.
The former exists in the far-flung future of the 31st century. A time when humanity has spread across a good portion of the galaxy, populating thousands of worlds. Control of these worlds is split between the noble houses and the clans. Each controlling anywhere from a handful to hundreds. All locked in an everlasting struggle for dominance. Sometimes they enjoy a tentative, almost cold-war like peace. Other times, they'll be plunged into full-on conflict and destruction. Pitting their armies of soldiers, vehicles, and gigantic walking war-machines (Mechs) against their foes.
While I wouldn't exactly enjoy the 'war' bits, living in such an amazing time surrounded by such incredible technology, and civilizations that span the galaxy, would be mind-blowingly incredible.
Plus, you know....giant robots with lasers and such.
As for Torchlight, it's a world that exists in a time and place where magic and early technology collide. It's a mix of classic fantasy spellcraft and robotic steam-punk.
Despite the world often being on the cusp of destruction, often at the hands of some otherworldly force, the place would be beautiful. Filled with such strange yet amazing sights. Creatures of beauty and grotesqueness. Living machines. Tools of immense power. Feats of magic. In a way, it would be like the worlds of Bioshock and The Lord of the Rings combined; only far less grim-dark and more stylized.
If I HAD to pick one....I'm not sure I could. Both sound so amazing that, which ever I'd pick, I'd regret not picking the other.