When we have not had a car in the past, we packed as many snacks as we could fit into the checked luggage, and then supplemented with the DVC convenience stores or the Hess station (
the one by the Boardwalk, you can walk to it).
Here are some pictures as to what types of things are available at the DVC stores. Taken September 2011 at SSR.
As far as prices go, the Hess station has better prices than the DVC stores, but you have to take into consideration the time to get there. The DVC stores are just so doggone convenient, you know?
That said, now, we ALWAYS rent a car. Those of us with food allergies can't eat a whole lot at the Hess or DVC stores, so Publix is our grocery of choice (the one by Gaylord Palms is nice- we have been there a few times). Goodings is WAY expensive, if it's even there anymore. There's a Super Target,
Walmart, and Winn Dixie not too far away, but Publix is always my Florida grocery of choice

.
All of THAT said... grocery delivery is more convenient. In fact, I think I MET the Garden Grocer at Publix (by accident) last September. A lady overhead me talking to Disney on the phone, then telling my DH that our room wasn't ready so we should probably wait to get the cold stuff. Then she came up and told me to go ahead and get the cold stuff and leave it with Bell services in their fridges, because she's a grocery delivery service and does that when the rooms aren't ready or the guests haven't arrived yet. She was so sweet for telling us that and saving us back and forth trips to Publix.