The closest publix to AKL is at the Orange Lake shopping center. There is a large super target directly across the street from the Orange Lake shopping center. From AKL, make a right out of the driveway to Sherberth Rd. Take Sherberth to US-192, and turn right. The Publix/Target will be either 3 or 4 stop lights down 192.
Once you've shopped, retrace your steps back to Sherberth, but instead of turning left to go into AKL, turn right to get on Osceola Parkway. The 2nd stop light will be Victory Way, where you'll turn left, and then Art of Animation will be on your right at the first light.