Eat two meals per day rather than three. Instead of eating breakfast, lunch and dinner, grab a quick snack in the morning and make lunch and dinner your two formal meals. You can bring inexpensive breakfast items that don't need refrigeration, such as granola bars or dried fruit.
Pack low-cost, non-perishable snacks. When you're tempted to buy expensive snacks at the food carts throughout the theme parks, reach into your backpack or bag instead. Not only will you save money, but you'll also be making a healthier choice. Mickey ice cream bars might look tempting, but they're loaded with fat and calories.
Travel at a time of year when the free dining plan is offered. During slower times of the year, Disney World often has a vacation plan that includes free meals. By taking advantage of this offer, you won't have to worry about the cost of food because it will already be fully included.
If you're staying at a suite hotel, take advantage of the cooking facilities to eat meals at your hotel. This can serve a dual purpose. Besides saving money by buying groceries and cooking your own food, it will force your family to take a break from the theme parks. This break can help you rest up and be less stressed overall versus pushing yourself with commando-style touring.
If you have a rental car, eat some of your meals offsite. The area surrounding the Walt Disney World resort is full of low cost buffet resturants where you can fuel your body at a budget cost. If you're staying on Disney property, you won't have an option to eat offsite. If you have your own transportation, it's an easy drive to get to the restaurant strips on 192 and other nearby areas.