The nearest Publix is on International Drive. Not far as the crow flies, but to get there you have to get on Vineland and circle around, about 7 miles or so, not what you have in mind I'm sure.
I think the nearest regular Supermarket to Disney property is a Winn Dixie at 11957 S. Apopka/Vineland Road (SR 535), about 3 lights north of the intersection with Hotel Plaza Blvd. (about a mile or so north of Goodings.)
If you want to stop on the way from the airport, I've heard a lot of people use Albertsons at 12981 S. Orange Blossom Trail (Orange Blossom Trail exit from SR 417).
I don't blame you for wanting to find an alternative to Goodings. I walk in there and my wallet starts to whimper.