Publix began with a store in Winter Haven, Florida, which opened in April 1930. A corporate HQ was established in Lakeland, Florida, in 1951. The chain expanded into the South Florida market in 1959. Out-of-state stores opened in Georgia (1991), South Carolina (1993), Alabama (1996), Tennessee (2002) and Virginia (2017). 
Graphic from Publix Supermarkets

PUBLIX JUNIOR-ANCHORED SHOPPING MALLS:

*CORAL RIDGE PLAZA, Fort Lauderdale, FL (1962) [outparcel]
*HOLLYWOOD MALL, Hollywood, FL (1964)
*NORTHWOOD MALL, Tallahassee, FL (1969)