I would also suggest checking out the menus. (I even printed them onto index cards for each park, so I would know what they had at each place-- so if we were in the mood for a salad we knew to go here, a sandwich here, etc)
We do not set a budget for food, but are always frugal about everything we buy. On arrival day we go to the grocery store and stock up on breakfast items, cheese, nuts, fruit, and drinks. I bring a dinosaur cutter and we make little PB&Js for snacks. We bring snacks in our backpack and only drink water in the parks. (We use hydration backpacks and fill them with ice. You can also get free cups of ice water.) We have milk, juice, and soda in the room. We return for several hours in the afternoon each day for a nap, so we have the chance to eat some food in the room and refill our backpack with snacks for the evening.
We often do not buy a full CS meal for each person. DH and I do not feel like eating much when it is hot and our little kids prefer to snack throughout the day. We will often get two or 3 adult CS meals and split them and then get something else a few hours later. When we stayed at Pop, we also got a full-sized pizza a few nights.
Our first trip we spent a total of $400 on food for 9 days. About $150 on groceries and $250 on CS. I certainly wasn't trying to deprive anyone of food or limit us to a certain amount. We just bought things as we were hungry-- and we even got Mickey ice creams a few times. That said, $400 is pretty cheap and I would budget for more than that.