Tardin-
Hmmm, your little one might take the Picky Eater Prize! DS has no problem carbo-loading with cheese crackers, Combos, chips etc, so we took those along to snack on, but most of his "staples" (string cheese, yogurt, fruit) are hard to carry along to the park. We tried to load him up whenever we were in the room. He will sometimes eat cheese pizza, but did not like the way any of it looked. He only likes 2 brands of yogurt or Gogurt. When he was 2, I never in my wildest nightmare though he would still be like this at age 7! (yesterday was his birthday!)
I try to be sympathetic, but sometimes we say, "Tough luck, just sit there while we eat if you don't like anything. We'll get you something later!"
I did see grilled cheese and PB &J on some of the kid's menus.
Good luck, and take lots of her favorites to your room!