What is the diameter of a city? We define the diameter as the 95th percentile time to get between two randomly chosen places in the city.1
In general, the diameter of a city increases with the population of the city. The diameter of Story City, IA (population roughly 3000) may be 5 minutes. For Des Moines, IA (metro population roughly 500 thousand) it may be 25 minutes. For Los Angeles, CA (metro population roughly 10 million) it may be 90 minutes. This is, roughly, a cube-root correlation. Which makes sense; there are three dimensions a city can be built-up in.
However, there is a fourth dimension: the dimension of technology. Without the train and the automobile, the diameter of a city with a given population would be far larger.
But the technology used in all these cities is essentially the same: the private automobile. Surely, with the potential for capital investment, and the ability to design the city (rather than for it to emerge), large cities should have potential for even faster travel?
I do not expect to have the opportunity or desire to build a city. But the question of “where” and “how” is still worth asking.
Internationally, most new cities are capital cities. There were some built in the United Kingdom in the 20th Century, such as Milton Keynes. While there are many cities that are building out more sub-urbs, there are virtually no New Towns in the United States from after 1945. The best example of city-building in the United States today is Burning Man, which is effectively sui generis in this regard; most cities are not built on perfectly flat ground, in the inhospitable desert, with no public utilities, and the expectation of being temporary.
But what would be different if you were to do a green-field build-out of a million-person city? This is rather different from just playing SimCity (or its more modern cousin Cities: Skylines), there is no intention of building the city to be iteratively feasible. This is not a new question (note The Guardian for one example), though Wikipedia’s coverage of theories of urban planning is extremely lacking.
Would it have a single Central Business District? Or would it have multiple centers?
While you can imagine a “post-private-automobile” vision of a city, it’s far more difficult to establish a vision where there are no trucks. For deliveries, for construction, for emergency services: it is clear that it cannot avoid some motorized vehicles.
Where should the city be? The city should be somewhere near abundant fresh water. With the current state of global warming, it should be at least 300ft above sea level. Beyond that, climate is the main concern.
What should the target density be? Should we actively try to minimize the land usage, or use as much land as feasible?
How should “public space” and “private space” be divided?
The radius of a city is not exactly half of that; it is the 95th percentile time to get from the city center to a random place in the city. There is quite a lot of interesting math with topology and statistics and cross-sectional bandwidth here that we will entirely skip over.