One story is that the place needs to be built on a high-margin industry. That high-margin industry leads to people with a lot of money who then want to flaunt it. They flaunt it by patronizing artists and scientists and donating to universities. People then come to that place both to try to become whales and to feed off of the scraps from the whales.
Is this pattern dependent on non-violent profit disciplines? Even in the ancient world, the examples (Athens) seem to be places associated with trade instead of war (Macedonia and Sparta.) Culture is explanatory dark matter
Places where this pattern matches
This requirement explains why early 21st century Berlin is not a Florence. It has a lot of world-class cultural disciplines but no world-class high profit discipline.
If this is true, there is also an inherent tension around prices. World class cultural disciplines do not often pay well. The average artists, writers, inventors, etc do not traditionally make a lot of money. Therefore in order to be in a place they need inexpensive costs of living. On the other hand, if a place has a world-class high-profit discipline it means that there are going to be a bunch of people making a bunch of money. When people make a bunch of money in one place, prices tend to increase. These increased prices make it hard for the world-class cultural discipline to exist.
This narrative has two consequences:
First is very practical: A Florence needs accessible low-cost-of-living lifestyles
Second is that inevitably Florences are going to have a lot of inequality.