Craziness. I live in a mid-size city in the midwest and we recently bought a 4,000 sq ft house for a little over your annual income. This is why I'd need a 7-figure income to live somewhere like NYC or much of Cali.
I don't consider any of those to be "mid-sized" cities other than maybe Madison, but looking up definitions of city sizes it looks like I could be wrong. I actually live in a suburb of what I consider a mid-sized city (pop ~500k) that's about the size of Akron. But yes, you can find offers like that in mid to larger cities in the midwest. Example job I interviewed for:
Inpatient averaging 18-20 patients a day. $250k base with significant RVU bonus (lowest paying physician in group was still clearing $450k, most clearing $500k). Weekend call Q4 weekends, full benefits and loan repayment. Position is still available. In midwest city of ~500k people with low CoL where I did residency. For reference, we rented a 4 bed 4.5 bath 3k sq ft house for ~$1700/mo.
Another example: Outpatient, inpatient, or mix. 30 minutes outside of the same city. 30/60 for f/up/new for outpatient. $325k base, $50k sign-on bonus, $150-200k guaranteed loan repayment. Full benefits. I did not interview or apply for that position, but a resident in the class under me signed on with them.
I also did med school in the same city I did residency and rotated through several psych facilities and offices there. The above was not unusual from those in the area I talked to.