One of the most famous post-apocalyptic world from a Final Fantasy is Spira, a world ravaged by Sin.
But I think all of the Final Fantasy worlds take place in a post-apocalyptic world. I don’t mean apocalyptic. All Final Fantasy worlds are apocalyptic as well. Most notably, Final Fantasy VII has the advent of a meteor threatening to destroy the entire world. Of course, each Final Fantasy has this type of catalyst propelling our heroes to save the world
But by post-apocalyptic, I mean a world or civilization after a catastrophic disaster already took place.
Take a look at Ivalice in Final Fantasy Tactics. The Lucavi leveled the civilization and other races (Moogles, Bangaas, Vieras, Seeqs, etc) went extinct. They treat machines as ancient wonders rather than modern technology, while airships were a legend of the old. The world before Final Fantasy Tactics? Final Fantasy XII.
So many Final Fantasy stories actually have legends about a great war that destroyed civilizations. Take a look at the Great Magi War in Final Fantasy VI:
Or even the Sorceress’ War in Final Fantasy VIII:
With no hero to save the world, civilization fell. We play in a recovering world, threatened once again by evil.
Japan has experienced its own catastrophic disasters throughout its history as well. In a sense, the developers write from what they know.