Presto! surcharge-free ATM access at all Publix store locations. Publix, which operates the Presto! network, has nearly 900 stores in high-traffic areas that are frequented by locals, vacationers and seasonal residents alike. The stores are located in five states – Florida, Georgia, South Carolina, Alabama, and Tennessee. More than 650 are located in Florida alone. Locate a Presto! ATM.