This might be a source of better metrics:
Northern America: Current Cost of Living Index by City (numbeo.com)
Using Cost of Living Plus Rent Index as a measurement, the Bay Area is the top in the US (occupying spots 2, 4, and 11) and Chicago is number 18. So definitely well down in the list. St. Louis is #98. Houston is #77.
Many years ago, I decided I needed to find new employment. One of the labs I interviewed at was in Pittsburgh, PA. When they sent me their offer, it represented a significant cut in pay (I was working in San Diego at the time). So I called the HR contact listed on the offer letter and explained that their offer represented a pay cut for me, which made it hard to keep their offer in consideration, since if I took the job and it didn’t work out, I’d be handicapped in joining a lab elsewhere. But, if the offer could be raised to my current salary (which I provided at that point), I’d give their offer serious consideration.
About a week later, the HR person contacted me and explained that they couldn’t match my salary. In order to do that, they’d have to pay me the same as the Director of their lab! So, at that point, we regretfully parted ways (I was serious about considering them if they just matched my salary, and I was getting offers at 10-25% over my current salary elsewhere.)