I don't know if individual store hours are shown on the Publix website, but you might look there.
Obviously, all of the stores are subject to local city and county regulations, so the days and hours of beer and wine sales may vary. Here in Miami, Publix stores sell beer and wine whenever they are open, except for Sunday morning. On Sunday, they can't sell alcohol until Noon.
ETA: Another option would be liquor stores or some drug stores. Many drug stores (Walgreens, CVS, etc.) sell beer and many of those are open 24 hours. You will also find many convenience stores open late, possibly 24 hours.