If you are staying in a family suite at the Art of Animation there is not a grocery store (some of the value resorts have a small grocery store). The Garden Grocer is a perfect for grocery shopping for whatever you need in the kitchenette. Garden Grocer allows you to order before your trip and deliver your groceries when you arrive to your hotel.
If you are looking for a delivery service for groceries this is THE website. They go above and beyond to make sure you are satisfied with your order.
Great food delivery to Disney hotels.