Brazilian Cities for Natural Birth?

That would be up to the doctor and the hospital regulations.
Main concern is health insurance. Emergency would not be turned away at a SUS, but child birth may not be an emergency. You will need heath insurance in any case.
As the heath care system is under much pressure and now with the virus  overwhelming the system, who know what the future will look like.
In the past a trucker strike shut down many clinics and many hospitals had no medicine through out Brazil.

Gotcha I have insurance that will cover a birth in Brazil, however the issue that I've encountered is private hospitals overwhelmingly learn towards c- sections. According to some articles the rate is pushing higher than 80% nationally at private hospitals. Ideally i'd like to find one that has an emphasis on natural birth if that even exists. Not sure if anyone knows of any which focus on natural birth in any of the Brazillian cities.

Private doctors push hard for c-sections because both they and many of their middle class patients want to be able to schedule the birth.  Finding a doctor who "has an emphasis" on vaginal birth in any major city will be hard; you'll probably be able to find one who's willing to do it, but you may need to talk to several, and gently but firmly resist some pressure.   

SUS is reported to go with vaginal birth whenever possible,  but will be crowded and noisy, and anesthetics are often in short supply.