Last year I divided our food money into separate envelopes, took only the appropriate one in my fanny pack each day, and left the rest in the in-room safe. That way I couldn't be tempted to splurge and mess up the budget. However, by carefully spending on meals, I had enough left over after 5 days, to have breakfast at Chef Mickey's on the morning of our departure.
I don't feel like we scrimped on food, either. I had budgeted $100 per day for our family of 6 (DH, me, DD 2, and DSs 16, 10 and 4). We ate at mainly counter service places for lunch, and some off site restaruants for dinner (Red Lobster, Steak and Shake, Pizza Hut). We had breakfast in the room (cereal, pop tarts, donuts, fruit, etc.). The $100 was more than enough with some good planning. I had made a list of reasonable restaurants for each park, what they served, and general price. I carried the lists in my fanny pack, and pulled it out when we were ready to eat. That way I wasn't tempted to eat at wherever place was nearby, but rather had a variety of choices, and their locations, menus, etc.
I also divided the kids money into envelopes, and carried it for them (except the 16 year old's). They were able to buy what they wanted, and I would tell them how much they had left. It worked well.
Hope this helps. Have a good trip! We will be using the same system on our surprise trip in December