I have the map here in front of me.
The rib place is called Smokey Creek Grill, it's located across from the Seaworld theater. Long lines form for this in the afternoon.
Next to this is Mama Stella's Italian Kitchen with Pizza, fries, and pasta. This might be a good idea. The kids could share 1 order of pizza and fries because they give you a mound of the fries.
Yes, they have burgers and fries, at the Waterfront Sandwich Grill, next to the sky tower. At this place, you walk up to windows, order, then take your food to tables outside. This may be what you're looking for, it's cheap.
There are many other places to eat, and they all have great food. Like Barry said, a good one is The Deli (hot and cold sandwiches) located in the far back corner of the park next to the Clydesdales. Get here early at 11am, because a long line forms.