As noted above by Niagara2, a new 54,000 square foot Publix opened near WDW just two weeks ago -- on Thursday, June 27, 2002, according to the Publix Web site. It's probably only a mile or two longer drive than to the new Winn-Dixie.
Publix
Regency Village Shopping Center
8145 Vineland Avenue
Orlando, FL 32800
From Hotel Plaza Drive, instead of going across the intersection at 535 into the Crossroads Mall (to Goodings) or turning left (toward the new Winn-Dixie), turn right. Go under I-4 and turn left at the Bahama Breeze restaurant onto Vineland. Drive past Orlando Premium Outlets (on your right). Vineland curves to meet International Drive -- and that's the corner where the new Publix is located (on your left).
The new Publix is open daily from 8:00 a.m. until 10:00 p.m.
I haven't been there yet, but I'm inclined to think that this will best place to shop when staying at a
DVC resort at WDW. It's only slightly less convenient than Gooding's or Winn-Dixie, and based on what I've seen at other new Publix stores (such as the Plaza Venezia Publix that BigTigger recommeneded), it should be a great store.