When we stayed there, we got onto I-4 and went west to the Rte. 192 exit going west. A couple miles out, near Orange Lake Country Club & Resort, there is a large Publix.
There is a Publix on the corner of 535 and 192. We shop there everytime we are at WDW. If you head towards Kissimee on 535 from the Vistana it is a few miles away and very convenient to get to. Turn left into the parking lot by the 7 11 and Burger King just before you actually get to the Publix for the easiest way to actually get into their parking lot.