Publix....go out Hotel Plaza Blvd, make a right onto 535 then a left after the Bahama Breeze. Head up that road past Dixie Stampede and Publix is on the left.
Its a nice store and you don't need a card. I've tried the Winn-Dixie and found that some of their prices were high....like canned soft drinks, etc....the stuff that tourists buy. Also Publix carries a good variety of natural foods.