I want to indicate that the setting of a story is Los Angeles in the 2030s, but I don't want to specify the year, and I don't want to write it as Los Angeles, 2030s
The Possibilities
Los Angeles, 203- (an en or an em dash)
Los Angeles, 203x or 203X
Los Angeles, 203_
Los Angeles, the fourth decade of the twenty-first century
Los Angeles, 203? (courtesy Loren Pechtel)
Which would be the most effective way to convey the idea?
Honestly I have to say 203-, 203x, and 203_ (your original first three options) are simply terrible in my opinion. Since none represent a widely used convention there's enough ambiguity in them to make reading them clunky to read and even worse if someone actually tried to read the text aloud. Try it yourself - reading something out loud can be a very effective tool for seeing if something you've written parses well.
You don't specify why you don't like the "Los Angeles in the 2030s" option but I have to say that actually would be my preference, mostly because it actually represents how people would actually refer to such a time period.
For example when people talk about say Disco, they talk about it being popular in the 1970s they don't say "It was popular in 197x" or "It was popular in 197underscore".
Of the four original options you gave only "the fourth decade of the twenty-first century" actually parses well - and I would say it's needlessly wordy compared to just saying "2030s".
If the time period is generally unimportant to the plot, I wouldn't specify at all.
Give some context clues, if you like -- have a character comment on how "retro" 2000s pop culture references are, or something like that. It makes a neat little easter egg for attentive readers without putting the date front-and-center as a direct announcement. I tend to find drawing attention to hard and fast dates like that are more trouble than they're worth: nothing ages faster than the near future, so it's only going to be a few years before whatever predictions you end up making become as outlandish as flying cars in 2020.
No unkindness to your concept, of course, but it tends to be excessively costly to work with for less payoff.
This is Anthony Trollope's solution:
Our hero in the autumn had written to Mr. Monk on the politics of the moment, and the following had been Mr. Monk's reply:—
Longroyston, October 12, 186___. My dear Finn,
From Phineas Finn, at project gutenberg.
My preferred option, if you don't like 2030s, would be Sometime after 2030. Often, there might be some event that occurred in the imagined history of the story that is used as the reference point, as opposed to the arbitrary decade:
A few years after the Big Crunch of 2028, we found ourselves sitting in a café on the Rue de Montplaissant sipping café lattes and slowly savoring macarons while the sky smoldered like the ashes of my last relationship.
or
I spent the years following the creation of the Hellenic Autonomous Zone for Androids, Robots, and Drones drifting from town to town, interviewing the residents and learning how the other side lived.
Tying the story to the major event seems more natural than tying it to a specific numerical year, as that's what we'd really do assuming there was a major future event - I imagine quite a few people describe the period from 2001-2005 as "In the years following 9/11", for example, and the late 1940s are commonly referred to as the years following World War Two, rather than the "late 1940s".
If you don't want to state the time setting at the beginning of the story, you can choose seomething which happened about 2015 and have a character mention it as something which happened about 20 years earlier. And maybe another character mentions something which happpened in 2010 as being over 20 years earlier. And maybe someone mentions that Y2K or 911 was about thirty or forty years ago.
But if you do want to state the time setting at the beginning fo the story, but not specify the exact yearI don't have much advice.
"Los Angeles 203__" seems the most natural to me.
Or maybe "Los Angles, the Twenty Thirties".
Or maybe "Los Angeles 20 minutes into the future".
TV Tropes - warning, a great time waster - has a trope called "20 Minutes into the future".
The Future, but not so far into it that you'd notice except for the abundance of Applied Phlebotinum.
Both Max Headroom and Brazil lampshade the Zeerust problem by setting themselves explicitly "20 Minutes into the Future" and "Somewhere in the Twentieth Century", respectively (rather than identifying specific dates), and by mixing up production designs and costumes that would have been considered "futuristic" in the '80s with random elements from previous decades.
The one I have seen used typically is the second option: "Los Angeles, 203X". However, this is mostly used if you have a story ubicated on a distant future or past.
If you just don’t want to reveal the exact year because it´s not important, use the fourth option: "Los Angeles, the fourth decade of the twenty-first century."
It’s a bit of a mouthful, but it works and feels a bit more natural.
I would suggest that the date be written with vague decade and a point in time it may culturally cover. Generally, if the year was in the 2030s I would say "Los Angelos, 2030s) with an "Early," "mid-," or "late" tag to better indicate the general year of the decade. Generally, early marks the first 4 years (2030-2033), "mid-" marks the next 3 years (2034-2036) and late marks the final 3 years (2037-2039).
Its important to note that a decade and the culture associated with it are normally not immediately known (The early 90s will still feel closer to the 80s than the mid to late 90s, which is where the 90s broke out into it's own thing) and the initial decade trends might have their formation here (For example, first 2 years of the 2000s still felt like the 90s... it wasn't until 9/11 that the 2000s got their general feel of the period) and often a cutural decade in the United States will tend to follow the Presidential term better than the actual ten year period in time (The 80s are generally Regan/Bush SR. period (1981-89 89-92), The 90s would be Clinton (93-2001), The 00s would be Bush Jr (01-09) and the 10s would be Obama/Trump) (09-17, 17-21).
Generally, a future date of 203x is more video game dating than writing and was often seen in early video games and often with more than one X (20XX or 2XXX) and generally showed that they game wasn't committed to a date other than it was quite far from the release date of the game. Having the first 3 digits of the year doesn't mask about when the future setting is and while tech will advance between now and the 2030s, it's not by an unpredictable amount of time (we won't likely get affordable flying cars by the end of the 30s).
I agree with the other answer that says that 2030s is fine. However if you don't like to use that for whatever reason (perhaps it doesn't fit the style you are going for), another option is to use a range.
Los Angeles, 2030–2039
However this does not indicate that it's a specific year in that decade. You could just prefix it with something like "some time in..." like this:
Los Angeles, some time in 2030–2039
Obliquely. The answer to your question about how to best establish that your story is set somewhere in the near future without being explicit, is to obliquely tie it to a well known event in the past.
Without knowing more about your story, its hard to make more precise suggestions by the idea is to have something in the story that a character can comment on or react to "It has been more than thirty years since the twin towers fell, why are people ... <insert something that reveals character qualities, advances plot, or builds on what is at stake in the story."
or "the pandemic was over like ten years ago, or there about, ... <insert same idea about character, place, setting, stakes, tension, whatever you want>
This is a general worldbuilding technique that will always let the story teller provide details to the reader in a way that feels very natural without obvious exposition.
