We always take breakfast food and snacks to help us stretch our food budget. Staying at RPR (and express pass) is worth it!
You've got some great suggestions above, but I'll throw in some of mine.
Depending on your budget, don’t rule out eating in the park entirely. Our eating philosophy in the park is that we don’t want to become so full that we can’t hop on a coaster soon after, so we eat smallish anyway, by sharing meals and eating less more often. If we are hungry after we eat, we pull out a snack.
Are you going to be able to eat before, but the day of check in, when you're back at the hotel and settling into your room in the evening, try the Shipwreck Nachos at Bula's pool bar. $10 for no meat (but does have black beans), $14 for chicken. It feeds our family of 4.
Table Service restaurants can be some of the best places to find cheap eats! Refills on drinks or a cup of ice water is better than the quick service prices. Mythos at IoA has an amazing Tuscan Tomato Soup for $4.99 for a bowl and they serve great bread. We like to eat here for lunch. Sometimes we will add in an appetizer like the Spanakopita Dip to share. Dessert shots for $1.75.
The Dining Plan Card can be stretched at quick service places to be a good deal too. It’s $21.99 and gives you a meal with a drink, a snack and another beverage. We eat somewhere like Thunder Falls at IoA and share a chicken and rib platter and drink ($15.99 + $3.29 = $19.28 plus tax), then we have a drink credit and a snack credit left (we use the snack credit on a butterbeer to share ($6.99). So for $21.99 we have a meal for 2 and a treat.
The Refillable Popcorn bucket is $6.49 for the first time and your refills are only $1.59.