The problem with the "Children of Man" scenario is that everyone dies off within a generation, unless we want to get spoileriffic. Let us assume, just off the top of our heads, that not everyone is sterile, and the few non-sterile people gather into small self-sufficient enclaves away from the general chaos. As the "old people" die off, the power grid goes offline, water and other utilities stop, gasoline and petroleum products become scarce. These enclaves might keep their own generator going on animal manure, but the first priority will be to raise their own food. Gradually they'll decay to a medieval lifestyle, with the occasional raid into the city. That's when I'd like to pick up.
However, I still need interesting challenges, besides hostile tribes competing for arable land. Surviving aliens, Von Neumann robot invaders, and a last-ditch attempt to breed human-ape hybrids all work, although the first two could easily get too powerful for medieval humans, even with submachine guns, and human-ape hybrids get into "swarthy foreign invaders" territory.
Another possibility is if the medieval-tech humans came from somewhere else:
- Portals through time drag humans from various eras to the desolate ruins of modern civilizations, a la GURPS Banestorm. Who created the portals, and why?
- Recycling an earlier idea, human colony ships return to the ruins of Earth, but lose everything but their lives when their ship crashes on re-entry. They must survive in a hostile landscape with only the clothes on their backs, a few salvaged low-tech tools, and what they dimly remember of primitive weaving, pottery, and metalworking.
- Instead of our world, humans in some other world find the remains of an earlier, technological, and perhaps nonhuman civilization.
"On two occasions I have been asked [by members of Parliament], 'Pray, Mr. Babbage, if you put into the machine wrong figures, will the right answers come out?' I am not able rightly to apprehend the kind of confusion of ideas that could provoke such a question."
- Charles Babbage (1791 - 1871)