I think goodings is the closest grocery store. We stayed at POR once and walked there and took a taxi back. It cost approx.$15 ( 2 years ago). We took the bus to downtown disney aand walked from there.
A few things to keep in mind though:
1) depending on what you need it may be cheaper to rent a car ( about $40) for the day and going to a walmart....goodings is not cheap
2) Unless you need alcohol, and alot of food, we don't think we saved anything buying sunscreen, snacks etc by going there instead of using the gift store.
3) You can also use Garden grocer.
I hope this helps!