Here's a list that ranks American cities by the size of their 'urban core' in relation to the entire metro area:
https://www.newgeography.com/content...city-dispersed
Some things to take away from the list:
Sunbelt cities such as Charlotte, Houston, Nashville, and Phoenix have virtually no historic urban core to speak of.
Sprawling Midwestern cities- Indy, Columbus, KC, have a small urban cores, but still larger than the sunbelt and sunbelt lite cities, with KC having the largest and Columbus having the smallest. Richmond has a smaller urban core than all three (in proportion to their respective metro areas).
The old Northeastern cities generally have the largest urban cores, followed by the old Midwestern cities, and then LA, Seattle, Portland, and the legacy Southern cities of Louisville and New Orleans.
Do you agree with this list?