There are three Publix supermarkets close to WDW. I don't usually go to Publix because they close early, if I need groceries I go after a day at the parks when everyone else is in bed. So I usually get my groceries at the 24 hour Super
Walmart on 192. They have some nice Disney stuff at the Super Walmart that is well made and lots cheaper than at WDW. Blankets, towels, clothing, toys, etc, you should make a point of checking it out.
Here are directions to the Publix that I know about.
1) Take the US192 exit from the park going East. Head toward Celebration 192. Publix is on the left, Celebration is on the right. You might pass it because it is not directly ON 192, but down a side road, but if you go as far as Old town, you ahve gone past it.
I wish I knew the names of the side streets to help you more, but it is not hard to find. It is down the side street where Walgreens is, so if you see Walgreens on your left, then take that turn and you will find Publix.
2) Go out the DTD Hotel Blvd exit and take a right. Proceed down this road for about 4 miles, maybe more. Publix will be on your left.
3) Get onto US 192 going West. Keep going down about 3 miles and look for the Orange Lake shopping Center. Publix is in this shopping center.
Hope this helps a little.