There was a Winn Dixie and a Piggly Wiggly nearby when I was growing up, but the local Publix was closer to the heart, probably in part due to church ties. Publix was close to the SBC and my father was a Baptist minister.
I also got the first album I ever owned at Publix, part of a classical music promotion in the store. Beethoven's 6th Symphony. I was five, I think.