There are lots of Publix supermarkets around. Click here
for a list. I go to Xentury City Center at the corner of 192 and International Drive (just outside of Celebration). They also sell beer and wine.
Directions: From Disney, take 192 East, past Celebration. Go past the Race Track gas station (on the left), under the bridge, then make an immediate left onto International drive. Make your next right into the Publix supermarket entrance. For a map, click here
Warning: Route 192 can get very backed-up after any of the parks close (7PM onwards), so I would not recommend going anytime in the early evening.