Yep, there is a Publix quite nearby.
When leaving the AKL, at the intersection of Sherberth (it's the first intersection after leaving the resort proper) take a right. Follow Sherberth to Black Lake (NOT 192). Take a right on Black Lake Rd. (there will be a Holiday Inn at that turn) and follow it until it intersects 192 west. Take a right on 192 west and Publix will be just down the road (Orange Lakes) on the right. If you want, you can continue further along 192 west to a second Publix also on the right. The second one is a bit smaller though, and may not have the variety of selections and merchandise of the first Publix.
It is much more cost effective than Goodings (which will be on the left in the Outback plaza).
