If you're by the DTD side of WDW you have a Publix by the Orlando Premium outlets Vineland location,you also have a Winn Dixie just north of the Hotel Plaza blvd Disney entrance on 535.If you go south on 535 there will be a Walmart.If you turn left from Hotel plaza on 535 and then turn right to Palm Parkway it will become Turkey lake rd and you will first see another newer Walmart and then a Whole Foods at the Turkey Lk rd and Sand Lk rd intersection,if you turn left on Sand Lk rd you will also have another Publix in that area which is known as Restaurant row.
If you're staying on the west side of WDW by AKL and the All Stars you might want to exit WDW by Sherberth rd and go to a very good Supertarget that's on 192,when you hit 192 go west from Sherberth rd.If you go a little further there's also a Publix on 192.
I go to the Publix on E Orange Lake Blvd. I do a pretty big food shopping when we come yo WDW and they have pretty much everything on the shopping list
We go to the Winn Dixie as we always stay at Fort Wilderness and you can sneak out the back way to it.... Bonus is the ABC Liquors right beside it. Lol