You're going to get a broad range of answers to this question. Obviously, it depends on what type of meals you anticipate having - mostly counter service, mostly sit-down, character meals, buffets, etc.
On our last trip in November, my wife and 7 yo daughter averaged $18/person/day. We ate breakfast in our suite with food we bought at the supermarket. Lunch and dinner was mostly counter-service though we did a couple of nice sit-downs during our stay. Also from the supermarket, we bought snacks to carry with us during the day to cut down on the pricey in-park snacks. We still did stuff like popcorn and ice cream, though.
So bottom line, our trip cost us $54/day for food for the 3 of us.
Steve