You could also rent a car for a day, Enterprise (on Katella) picks you up from hotel and when you drop car back off, they bring you back. I use Entertainment coupons for them and book online for about 17.00 a day with coupon. You can then do your own grocery shopping (and if you want to visit somewhere else in the area you can.) I always rent cars right from the airport but have occasionally gotten a shuttle to disney then use Enterprise for a day or two. There are two Vons (grocery store) in the general vicinity of Disney. You can even apply for your Vons card online, bring the application with you and get discounts. Von's probably also delivers. The one on Lincoln Ave (off Harbor Blvd.) is open 24 hours.
Also within walking distance you can get snacks. Just walk out of Disney straight onto Harbor, cross street by where all hotels are. There will be a Dennys, and IHOP. The hotel (I believe Park Vue) has a store on the side that sells snacks, soda etc.