Publix is quite close. Coming from OKW, just turn left at Wide World of Sports (Osceola) and then right at the Gaylord Palms. It's about 1KM from there on your left.
we usually take a cab over to the Winn Dixie from OKW. Cost is about $20-25 return. We have a Winn Dixie discount card, so we save $. They let Canadians sign up for it.