There are lots of good suggestions here. The only thing I would add is fresh fruit. I see a lot are mentioning fruit cups, but we have taken apples, bananas, oranges, and even grapes (I wash them and put them in a small tupperware or baggie).
I bought a lunch bag from Kroger which was a bit bigger than a kid's lunchbag but not so big we needed a locker. It held an icepack, a couple drinks, our sandwiches, and some yogurt (food for 3 people). Things that didn't need refrigeration like granola bars I didn't stick in there if they didn't fit. All in all, we were able to take decent lunches into the park, they stayed cold, and we got full. This really saved us on the food budget as we stayed off site and didn't have a dining plan.
Other times, we ate a huge breakfast, took a small snack with us, and headed out of the parks by 1pm for our afternoon break. We then ate back at our time share which had a full kitchen. This allowed us to make another large meal so that we could head back to the parks full.