In terms of quality, Atlanta has world class hospitals - some of the best in the country, including the Emory system, connected with the university, Piedmont hospitals, and several more major, top quality healthcare groups.
As far as cost goes, the healthcare system in America can be confusing and is currently in flux. Buying services outside of an employee-sponsored group plan can be expensive no matter where you are. The cost of medical care is less a function of the facilities you go to and more a function of the health services plan you get. The healthcare.gov blog is probably the best place to look around for how you can participate in marketplaces for health care depending on immigration status.