If you have a car, getting to the Publix or Super Target on 192, just before 429, is easy. Exit main AKV gate, take first right onto Sherbeth Rd. Take Sherbeth to 192 (Irlo Bronson memorial Highway), turn right and drive until shortly before 429 and turn when you see it (Target on left, Publix on right). The distance is only about 3 miles.
Some have asked about the possibility of just walking from AKV to Publix, a distance as the crow flies of a littler more than 1/2 mile. It cannot be done because you need to go through woods and swamps and there is an outer perimeter fence blocking the ability to exit.