Hi Christine!
I know about picky eaters. I have one in my family (not me of course, I eat EVERYTHING-smile)...
If you plan on doing any eating at the resort or parks, you can't go wrong getting a meal plan. Disney offers 3 good meal plans: Quick Service Dining, Standard Dining, and Deluxe Dining.
Compared to out of pocket, you will save 20% choosing Quick Service, 30% savings for Standard, and 40% savings on Deluxe.
Each plan offers a multitude of variety and restaurants to choose from. For our picky eater, my son, we would make sure to go to those restaurants that had some of his favorite foods, or at least the places with food he was less picky about. Since all the plans include snacks, we would bring a snack along our son liked, in the worst case nothing on the menu works for him. We also got lucky at some stops, the hungrier he was, the less picky he became (smile).
I encourage most families to at least get the Standard Dining Plan if it fits in their budget. That Plan includes 1 table service, 1 quick service, and 1 snack per person per day. The table service is the key: 1 meal per day you deserve to be treated to a sit down service. Disney table service restaurants are excellent! You also can get a character meal, which, if your picky eater is a kid, may like seeing a character walk up to their table.
For more information, click the following links below. Each page has a PDF with the list of restaurants that match your dining plan.
Quick Service
Standard Dining
Deluxe Dining
Good luck!