You'd think it would be easy to find what you are looking for, but it's not. I've had this problem even with a small "group" of 3 kids, none of whom wanted to eat what the other one(s) wanted!
If you are in California Adventure, one idea is to go to Whitewater Snacks inside the Grand Californian. It sounds far away, but it really isn't (right across the path from Grizzly River). They have chicken fingers, pizza, hot dogs & chili dogs (no corn dogs), hamburgers, great nachos, grilled cheese, chicken sandwich, turkey sandwich, PB&J, and so much more. Honestly, I don't see how you can beat it as far as variety goes. And the other great thing is that it always seems to be calm and quiet in there, with plenty of seating. They bring your food to you once you order, which is a huge advantage over regular counter-service.
I can't think of a place in
Disneyland that has as much variety. One option would be Tomorrowland Terrace (burgers, chicken nuggets, turkey sandwich), and Pizza Port (pizza, pasta) is right across the walkway so you could divide and conquer and meet back at the Terrace to eat.