I am shocked by this as I find it's the opposite for us kiwis. We love America, Americans and Disneyland but find the worst part of the trip is always the food. Everything is so processed and the whole familly starts to feel a bit ill and sluggish after a day or two. (and POTC) experience.
Processed foods are common at large public centers such as Disneyland. Take a drive to one of the local restaurants outside the Disney area for far better food.
I took a friend from Australia to Disneyland a few years ago and she hated the food just like you! What I found though was that she preferred very bland, very plain foods. Sandwiches only on plain white bread, never any kind of fancy rolls etc. Hated any food that had more than just salt and pepper spices. She loved the food in England which I could not stand. Too bland, flavorless and just blah!!
I really do not eat any fancy meals at Disneyland. Too expensive, not very good, crowded, noisy etc. We always drive a few miles away to a nice restaurant for far better meals.
This year the girls (age 11) want to go to Benihanas instead of a Character meal or other Disney meal. Theres one about 4 miles away so thats what we will do. They're all over the world and always a fun time and good food.

The one at Allears.net lists it under the lunch menu only.
The potatoes are also excellent. 

