Economic... Weirdtopia: The world has an indirect economy. People trade status for predictive power to decide which ventures get the most attention and which resources to allocate to whom/what. Businesses are considered a weird anachronism of a begone era. People are free to do whatever they want with their status, except trade real property. (They can, however, use it to make the market grant favours if they want.) Life's necessities are always freely accessible.
Governmental... Weirdtopia: Every conflict is resolved either by consensus or moving away. There are even seed spaceships moving far away from Sol for the latter option. Non-violence isn't the rule, it's the law. Every intelligence agreed to remove violent urges. Non-violence has an extremely broad definition that not only covers force, but also deception, market manipulation, even advertising, bad manners and ostracism. Honesty is not expected, it just is; the only way people find out what the word means is through history classes.
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:
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...
Sexual...
Governmental...
Technological...
Cognitive...