Hi Michelle! If you have a car, then ask at your front desk and they'll direct you to the nearest grocery store. There are several nearby, just outside of Downtown Disney. We always bring some staples with us such as cereal bars, snack foods etc. You can also buy fresh fruit, breads, snacks and more at the shop in any Disney resort.
If these don't meet your needs, then you might want to consider Garden Grocer, an online grocery store that will deliver your order straight to your resort room. Simply fill out the order form before you leave for your vacation, and your groceries will be delivered to you. It's quick, easy, and they are a reputable and reliable company.
Hope this helps Michelle!