Usually I just buy the basics at the Marketplace store at the resort - despite the fact that I drive to Disney and have my car, and there are groceries nearby, if it's not a long stay (under 5 days), I don't usually need too much - milk, juice, bread, eggs, a few snacks, etc. It just doesn't feel worth the drive for that. On rare occasions where I'm staying longer or with a lot of family, I'll make a run to a grocery nearby on the first day (used to love Gooding's...miss that place!) - usually the Winn-Dixie on 535.
(Of course the caveat for me is that I drive up, so I can bring much of my own supply...so sometimes I don't need much more than eggs & milk - the rest I can pack and bring in a cooler like sodas, teas, snacks, bacon, deli meats, bread, cheese, butter, etc.)