"Two roads diverged in the woods. I took the one less traveled, and had to eat bugs until Park rangers rescued me."
—Jim Rosenberg

Utopia and Dystopia have something in common: they both confirm the moral sensibilities you started with. Whether the world is a libertarian utopia of the non-initiation of violence and everyone free to start their own business, or a hellish dystopia of government regulation and intrusion—you might like to find yourself in the first, and hate to find yourself in the second; but either way you nod and say, "Guess I was right all along."

So as an exercise in creativity, try writing them down side by side: Utopia, Dystopia, and Weirdtopia. The zig, the zag and the zog.

I'll start off with a worked example for public understanding of science:

Utopia: Most people have the equivalent of an undergrad degree in something; everyone reads the popular science books (and they're good books); everyone over the age of nine understands evolutionary theory and Newtonian physics; scientists who make major contributions are publicly adulated like rock stars.
Dystopia: Science is considered boring and possibly treasonous; public discourse elevates religion or crackpot theories; stem cell research is banned.
Weirdtopia: Science is kept secret to avoid spoiling the surprises; no public discussion but intense private pursuit; cooperative ventures surrounded by fearsome initiation rituals because that's what it takes for people to feel like they've actually learned a Secret of the Universe and be satisfied; someone you meet may only know extremely basic science, but they'll have personally done revolutionary-level work in it, just like you. Too bad you can't compare notes.

Disclaimer 1: Not every sensibility we have is necessarily wrong. Originality is a goal of literature, not science; sometimes it's better to be right than to be new. But there are also such things as cached thoughts. At least in my own case, it turned out that trying to invent a world that went outside my pre-existing sensibilities, did me a world of good.

Disclaimer 2: This method is not universal: Not all interesting ideas fit this mold, and not all ideas that fit this mold are good ones. Still, it seems like an interesting technique.

If you're trying to write science fiction (where originality is a legitimate goal), then you can write down anything nonobvious for Weirdtopia, and you're done.

If you're trying to do Fun Theory, you have to come up with a Weirdtopia that's at least arguably-better than Utopia. This is harder but also directs you to more interesting regions of the answer space.

If you can make all your answers coherent with each other, you'll have quite a story setting on your hands. (Hope you know how to handle characterization, dialogue, description, conflict, and all that other stuff.)

Here's some partially completed challenges, where I wrote down a Utopia and a Dystopia (according to the moral sensibilities I started with before I did this exercise), but inventing a (better) Weirdtopia is left to the reader.

Economic...

Utopia: The world is flat and ultra-efficient. Prices fall as standards of living rise, thanks to economies of scale. Anyone can easily start their own business and most people do. Everything is done in the right place by the right person under Ricardo's Law of Comparative Advantage. Shocks are efficiently absorbed by the risk capital that insured them.
Dystopia: Lots of trade barriers and subsidies; corporations exploit the regulatory systems to create new barriers to entry; dysfunctional financial systems with poor incentives and lots of unproductive investments; rampant agent failures and systemic vulnerabilities; standards of living flat or dropping.
Weirdtopia: _____

Sexual...

Utopia: Sexual mores straight out of a Spider Robinson novel: Sexual jealousy has been eliminated; no one is embarrassed about what turns them on; universal tolerance and respect; everyone is bisexual, poly, and a switch; total equality between the sexes; no one would look askance on sex in public any more than eating in public, so long as the participants cleaned up after themselves.
Dystopia: 10% of women have never had an orgasm. States adopt laws to ban gay marriage. Prostitution illegal.
Weirdtopia: _____

Governmental...

Utopia: Non-initiation of violence is the chief rule. Remaining public issues are settled by democracy: Well reasoned public debate in which all sides get a free voice, followed by direct or representative majority vote. Smoothly interfunctioning Privately Produced Law, which coordinate to enforce a very few global rules like "no slavery".
Dystopia: Tyranny of a single individual or oligarchy. Politicians with effective locks on power thanks to corrupted electronic voting systems, voter intimidation, voting systems designed to create coordination problems. Business of government is unpleasant and not very competitive; hard to move from one region to another.
Weirdtopia: _____

Technological...

Utopia: All Kurzweilian prophecies come true simultaneously. Every pot contains a chicken, a nanomedical package, a personal spaceship, a superdupercomputer, amazing video games, and a pet AI to help you use it all, plus a pony. Everything is designed by Apple.
Dystopia: Those damned fools in the government banned everything more complicated than a lawnmower, and we couldn't use our lawnmowers after Peak Oil hit.
Weirdtopia: _____

Cognitive...

Utopia: Brain-computer implants for everyone! You can do whatever you like with them, it's all voluntary and the dangerous buttons are clearly labeled. There are AIs around that are way more powerful than you; but they don't hurt you unless you ask to be hurt, sign an informed consent release form and click "Yes" three times.
Dystopia: The first self-improving AI was poorly designed, everyone's dead and the universe is being turned into paperclips. Or the augmented humans hate the normals. Or augmentations make you go nuts. Or the darned government banned everything again, and people are still getting Alzheimers due to lack of stem-cell research.
Weirdtopia: _____