Edit: Not sure what the orbital path of the ISS is. I suppose it would indeed depend on where it is. The question would be: where in the path is more than ±417 KM away from a city.

//ignore Seems like the ISS is always closer. 400KM vs 817KM.

> The ISS maintains an orbit with an average altitude of 400 kilometres (250 mi) by means of reboost manoeuvres using the engines of the Zvezda module or visiting spacecraft.

https://en.wikipedia.org/wiki/International_Space_Station

> Alert, in the Qikiqtaaluk Region, Nunavut, Canada, is the northernmost permanently inhabited place in the world, at latitude 82°30'05" north, 817 kilometres (508 mi) from the North Pole.

https://en.wikipedia.org/wiki/Alert,_Nunavut

I always find it interesting that as I sit here on the south coast of England, Glasgow in Scotland is significantly further away (approx 450 mi) than the ISS when it orbits overhead. It's one of those details that shows that 'low Earth orbit' really does mean 'low'.

It is really well illustrated here https://what-if.xkcd.com/58/

Yes, I have always loved this xkcd and even once sketched a version myself to someone I was having a debate with.

But presumably the space station passes over the middle of one ocean or another, where it is not only 400km up but also some number of hundred kilometres away laterally?

There's a lot less of that very-distant ocean than you might think. You need about 700 km of lateral distance on Earth to get 800km distant from a point 400km over the surface.

Start drawing 700km bubbles from random specks of land in the ocean, and the uncovered ocean disappears quite quickly. Bermuda, the Azores, and Newfoundland conspire much of the North Atlantic between the US and Europe. Seychelles, the Maldives, and the British Indian Overseas Territories similar get a decent coverage of the eastern Indian Ocean. Random Polynesian islands also manage to provide a surprisingly good coverage of the South Pacific (almost contiguous all the way to Hawaii), although the gaps are more evident here.

I don't have hard numbers here, but I'd hazard a guess that the ISS is closer to civilization about 80% of the time--not bad, considering that civilization occupies far less than 30% of the surface.

But the ISS’s orbital path doesn’t take it much above Hudson’s Bay, or an I mistaken in that?

The ISS's orbit is inclined 51.6 degrees; the southernmost point of Hudson Bay is at 51.2 degrees latitude or so (from Google Maps). So the ISS just barely goes over Hudson Bay.

In Europe, 51.6 north is roughly the latitude of London, Amsterdam, Berlin, or Warsaw.