The Piedmont Urgent Care by WellStreet Difference WellStreet Urgent Care and Piedmont Health System have partnered to create the premiere Urgent Care group in Atlanta, GA and surrounding areas. Welcome to Piedmont Urgent Care by WellStreet. Our Quality Promise: We think it is important for patients to have confidence that their physician has specialized training. ALL our physicians are trained specifically in the specialty of urgent care medicine, so you can be assured of the highest quality of care and competency every time you visit a Piedmont Urgent Care. No other urgent care in the country has made this level of commitment.