Let's make a list, then narrow it down.
Here's the criteria to judge scenarios
- Kill off most people
- Make big cities uninhabitable
- Make food and clean water hard to come by
- Be predictable enough to evacuate world leaders
- Be plausible enough that it could occur in real life
Here are scenarios that won't work, but you could handwave anyway. Comment if you think some are worth elaborating on anyways:
- Natural pathogen: Extremely difficult to achieve #1 in the modern day
- Famine: Extremely difficult to achieve #1, #3 globally
- Planetary collision: Violates #1, #3, #4 by doing too much
- Infertility: Violates #2, #3, #4; violates #5 because it is treatable
- Gamma ray burst: Violates #1, #3, #4 by doing too much
- Vacuum decay: Violates #1, #3, #4 by doing too much
- Grey goo: Violates #1, #3, #4 by doing too much; violates #5 somewhat
- AI apocalypse: Violates #1, #5
Now let's talk about some approaches that might work.
1. Nuclear War
This is a promising one, and many organizations take it seriously. The idea behind this is that warfare using nuclear weapons would contaminate the environment, from weeks in some areas up to decades in others - and trigger catastrophic events that would cause more problems.
Consider that this could deplete the ozone, causing a "nuclear summer" and hot conditions, or release clouds of ash and particles, causing a "nuclear winter" when less light reaches Earth. Either is plausible.
- High mortality rate is inherent with radiation; if you hit the cities, it also kills a significant number of people
- Boom. We've taken care of the city inaccessibility part
- Contamination will be rampant! Food and water will have to be filtered / grown far, far away or sheltered from blasts (and in specific areas dependent on winter / summer scenario)
- If tensions escalate, yes, you can evacuate people.
- This is plausible! As previously stated, this is taken seriously.
2. Biological warfare
.. is the use of a (possibly engineered) pathogen, chosen for specific qualities, distributed in specific places, with the intent of causing as much harm as possible. If an organization with genetic engineering capabilities and enough money has bad intent, they can pretty much do this in real life already.
Consider a conventional bacteria or virus "plague" that spreads rapidly across the population, and lies dormant in corpses, making populous areas less safe. Eventually, cities may become safer, but for a while they will be contaminated.
Alternatively consider releasing a virus or set of viruses in major cities, parks, events etc. that causes rapid cancer in its victims. Gruesome, deadly, spreadable, and unique.
- If your organization plans it right, they can kill off most people
- Addressed inaccessibility above: cities have more corpses and more contaminated supplies
- See the above - any food or water that had contact with humans will either have been looted or contaminated
- This is reasonably predictable - if it is clear there is an intelligent person, group etc. causing the change, world leaders will feel threatened.
- This is plausible! Fully within the realm of modern science.
3. Climate change
... has been associated with rising seas (eliminates coastal cities), air pollution (remaining cities), the pollution of water, and making it harder to grow crops. Perhaps your show takes place in a world where we failed to save the planet, then most of us died, becoming scavengers in the ~desert~.
- May increase risks of cancer, diseases etc. as populations grow closer; could eventually lead to less people as there is less hospitable land
- Big cities will be the most polluted. Even after some years, they may not be safe to breathe in (or even comfortable)
- Less accessible farmland and more pollution will make food and water precious commodities
- Also predictable - not necessarily an instant "relocation"-type event but it could be workable
- This is plausible because it is based off of scientifically supported predictions
Perhaps astronomers discover that no, that asteroid we said will always just swing by is actually going to collide with us, and there's no way to stop it. Of course, it can be small enough to avoid a dinosaur-level extinction while still releasing a ton of heat, radiation, and particles, making life on the surface difficult, and prompting foreign leaders to move somewhere safer.
- Climate-related effects may kill a significant portion of the population
- Cities will be descend into anarchy close to the impact date; this could cause some serious problems that lead survivors to avoid them (bombings, etc)
- Less farmland, more contamination could result in less food and water available
- The basis of this event is a prediction; there should be time to evacuate your world leaders
- While the sudden discovery of an asteroid headed toward Earth is .. unlikely - it's not impossible.
5. Coronal Mass Ejections
The basis of the Maze Runner Series' apocalypse (spoiler), ejections from the sun are unpredictable and very hard to stop. They may result in a potentially hotter world, with damaged satellites and electrical systems. If you make your event sufficiently strong (unlikely but definitely possible), it could cause environmental damage and civilian deaths.
- If the event is powerful, sure.
- If the last major ejection to hit Earth severely interfered with telegraph wires (1859) imagine the damage to modern technology that would occur
- The loss of infrastructure, crops etc. may cause a descent into anarchy, making food and water precious commodities
- This is not predictable enough to move your world leaders prior to the event, but you could consider doing so before things descend into anarchy.
- This is plausible and a genuine concern.