About the only place I remember my Mother buying fabric when I was young was JC Penney, Sears and Wards and another dept store called John A Brown who had more expensive fabrics here in Oklahoma City. I also remember TG&Y but that may have been after Penneys and Browns stopped selling fabric.
I can't remember when they stopped selling fabric but I believe they all were still selling fabrics when My girls were small in the early 70's.