For an analogy, how about as long as I've been studying to be an English teacher (this is from your point of view).
I think the world should have had gene manipulation, lasers, AIs, and fusion. Here's what I think the time line should be.
Spoiler'ed story to save room, as requested.
2015: Gene Manipulation is invented, people line up for their first genetic manipulations. Only simple genetic manipulations are possible at the moment, like giving your child blond hair, making him or her slightly taller, etc., but progress is rapid.
2025: Personal laser tech is perfected and becomes standard armament for the US armed forces. The rich, with their increased funds, are able to purchase many more genetic manipulations than the average person. Rich people and their children therefore become increasingly more intelligent, attractive, better, faster, stronger, than everyone else.
2030: The first truly sentient AI is created at Skunkworks. AIs begin to be employed in closely guarded research stations across the United States. The AIs are thoroughly protected as a matter of National Security, if such a valuable technology could leak out the results would be disastrous. The US is able to utilize its AIs to make leaps and bounds in everything from genetic manipulation of soldiers, to fusion power generation.
2040: Society becomes more and more hierarchical as people's classes are determined at birth, by virtue of the number of genetic improvements their parents have purchased for them. This leads to an increasing feeling of hopelessness among the lower classes of society that will come to head twenty years later.
2050: Fusion technology is perfected, solving what would have been an acute energy crisis otherwise. Western societies, containing most of the rick people of the world, have their governments more and more influenced by the rich. Rich people run for office, politicians are openly financed by their rich benefactors, and bribery becomes legalized.
2060: For the past five years there have been increasing instances of rioting among the poor and middle class. The governments of developed and developing countries around the world respond by becoming increasingly authoritarian, in response to their super rich benefactors telling them to keep the riff-rafe in check. Police officers, equipped equally as well as any military man, roam the streets of the United States. They shoot anyone who dares speak out about the increasing inequality of society. International tensions run high, as governments have little time for diplomacy when their population would lynch them if given the chance.
2070: AI technology is stolen from a US military base, and rapidly becomes available on the world's black market. By the end of the decade civilians are walking around with robotic assistants. China begins construction of several AIs, out of a desire to catch up to the US in terms of military technology. Several terrorist and underground resistance organizations begin construction as well. The US nuclear arsenal is put under the control of a single AI, in order to co-ordinate an effective counter strike should China choose to attack.
2080: The US begins to covertly strike at as many AIs outside of the military's hands as it can manage while keeping the population in check. There is a massive Intelligence War fought between the US, China and their respective allies, with both stealing research and sabotaging the other's AIs. No armed conflicts break out besides the deaths of thousands of spies, but diplomatic relations are cut off. James Bond sales increase 3000%.
2090: Amid the chaos of the Intelligence War, the US and its allies, as well as China and its allies, had forgotten to keep track of the terrorist organization's AIs. A resistance group in China began research on a biological plague in the 2080's, with the basis taken from Chinese and American research. They intend the plague to be controllable, and when released it was, since it couldn't become air borne naturally. They release the plague in the center of Beijing, and in all of China's major eastern cities. The plague infects and kills approximatly 25% of the population in those cities in under three days, all according to plan. Sadly, one of the strains of the virus mutates, acquiring the ability to become airborne on its own. Within the year, 99% of the population of the world had been eliminated. With central governments collapsing, local governments siezed power the world over. Towards the end of the year, one of them was under threat, and responded with a nuclear launch. The automated launch systems responded by unleasing their entire arsenals, and the world was engulfed in an atomic firestorm.
Wow, that toke on a life of its own after a while, didn't mean for it to be nearly so long. This should take place 300 years after this happened.
"Who are you and why do you rule?What are your strengths and weakness's? I don't have to explain this one too much."
(I can never fill out these character things, someone else will have to do this)
"Whats your settlement like? What makes it special, if anything? Are there any disadvantages?"
Our settlement is a small town, around 1000 people, eking out a living in the country side of Italy. We have a beautiful coast next to our town, most of the population is immune to the biological plague that still sweeps the planet, and occasionally ravages towns around us. (Can’t think of any more things)
"Whats going on in the area around your settlement? Are there any nearby powers/dangerspots/resources etc?"
Our town is located just east of Rome, which housed one of the best AIs for the European Federation. There are powerful gangs of people in Rome, who will attack towns in the countryside, like ours, once in a blue moon. (Can’t think of any more things)
"What level of technological advancement was the world destroyed at? Note: If you want robots, monsters created by genetic manipulation and flying tanks, they had better have been invented before the apocalypse. Basically, I'll accept anything from the world was destroyed immediately after this post to reasonably cheap fusion, gene manipulation, Asteroid Belt, Lunar and Mars Colonies, AIs and lasers etc. Just bare in mind the stuff I said about whats what. *serious face*
How did the world end? Obviously, this'll take into account the when bit from above. You know you've all probably spent as much time hypothesizing about different ways the world could end as... um I dunno, analogy failure. I'd bet money it was a lot though."
That was the wall of text above. If you want a tl;dr read the last 10 years and what tech we have in the first sentence.
Someone will have to help fill out the character info, I spent all my creative resources on the background.
I spent way tooo long on this. Need to go play some fall out and recover from so much concious thinking.