I do the bulk of my shopping at Winn Dixie (the B1G1 free deals on their london broils, chicken thighs, & boneless skinless chicken breasts can't be beat. They're even cheaper than Costco sometimes) because their rewards program really does help you save and you get gas rewards for shopping which is great! But I do go to Publix to get my cold cuts because I don't like the Winn Dixie deli.
I split my shopping now between Costco (when we do a big meat purchase, usually every 2 months), Winn Dixie for most everything else, Publix for the deli & bakery stuff, and Aldi for certain sale items.