Leyrann
Deity
You come across upgrading units anyways because you cycle through units.
The entertainment indeed isn't automatically distributed, but the luxeries are distributed such that every city has an equal amount of amenities. Basically, imagine a container with at the bottom some solid that forms a few peaks. Then, you start pouring water onto it (typically more than you had solid). The solid is the base level of amenities, from entertainment, the water is the amenities from luxeries.
And if you really want to put those luxeries from a great person there where most amenities are required, it's always a safe bet to go for the biggest cities that are not covered by the colosseum. There aren't that many factors into amenities. Only entertainment districts (which should simply cover every city in your empire in lategame), luxeries and the colosseum give a lot of amenities, while only size (and war weariness, which appears in a small amount of recently-conquered cities, but requires you to war and therefore have a big empire with a lot of luxeries to divide between your cities) costs amenities.
The entertainment indeed isn't automatically distributed, but the luxeries are distributed such that every city has an equal amount of amenities. Basically, imagine a container with at the bottom some solid that forms a few peaks. Then, you start pouring water onto it (typically more than you had solid). The solid is the base level of amenities, from entertainment, the water is the amenities from luxeries.
And if you really want to put those luxeries from a great person there where most amenities are required, it's always a safe bet to go for the biggest cities that are not covered by the colosseum. There aren't that many factors into amenities. Only entertainment districts (which should simply cover every city in your empire in lategame), luxeries and the colosseum give a lot of amenities, while only size (and war weariness, which appears in a small amount of recently-conquered cities, but requires you to war and therefore have a big empire with a lot of luxeries to divide between your cities) costs amenities.