Assuming it's relatively reflective and good lighting, it should be visible at least all of north america. Probably northern south america, eastern asia. A bit under half the world would be able to see it.

> If someone builds a space elevator, what is its clear night visibility distance?

A bit less than a quarter of the way around the earth, since geostationary altitude is significantly larger than Earth's radius.

Strangely enough, Wikipedia's equations give nonsensical results in that they exceed Earth's circumference, but my own calculation using basic right-triangle math gives a far more reasonable ~9Mm

> If a station was grounded in Los Angeles

Can't.

Space elevators can only be built at 0° latitude (ie exactly on the equator) so its base would have to be in one of these countries

How many “good” regions are there? I assume some rock types would be unsuitable for anchoring (maybe it’s anchored so deep it doesn’t matter?) but definitely not near tectonic plates and presumably not in any type of water? Would need to be close to a major port or shipping hub, and probably some other criteria

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Mount Kenya National Park is the first space elevator y'all build and I remember seeing it from India.

> I assume some rock types would be unsuitable for anchoring (maybe it’s anchored so deep it doesn’t matter?)

Well the tension on the base station from the cable would be ~0 due to how the orbital physics work, and we're pretty good at deep-drilling to lay foundations for large buildings, so I don't see too many concerns there

> definitely not near tectonic plates

The Japanese have some pretty good anti-earthquake building technologies, like big shock absorbers in the foundations, plus the end of the cable could be anchored with a floating mount - so maybe not as much of an issue as you might think

> presumably not in any type of water?

The romans built stuff in water and we do too.

> Would need to be close to a major port or shipping hub

Those would be built as required if there isn't already a suitable one nearby - consider the financial allure of a space elevator, and the number of countries that are already making artificial islands and reclaiming land from the sea.

> probably some other criteria

The most problematic criteria is the strength of the cable (due to taper ratio) - we don't currently have the technology to manufacture the cable, although carbon nanotubes are theoretically strong enough to do the job if only we could work out how to extrude insanely long nanotube fibers en masse from a facility in orbit.