Hi, Brandie!
This is a great question, and it's one with which I have a LOT of experience; I advise hundreds of my students each year on this topic specifically, as they approach their Senior Trip to Walt Disney World. (I really LOVE this question! Thanks so much for asking!)
The Quick-Service restaurants with the most variety on the menus are as follows:
Magic Kingdom: Cosmic Ray's Starlight Cafe (in Tomorrowland, to the right of Cinderella Castle)
Epcot: Sunshine Seasons (in The Land, near the entrance to Soarin')
Disney's Hollywood Studios: Fairfax Fare (near the entrance to Rock 'n' Roller Coaster Starring Aerosmith)
Disney's Animal Kingdom Park: Flame Tree Barbecue or Yak & Yeti Local Food Cafes
We often have extended family and friends with us on our trips to Walt Disney World, and these restaurants always provide everyone with something that they are sure to enjoy. If you'd like to see what items are on the menu, check out allearsnet.com, which is NOT a Disney-affiliated site, but does a great job with listing (unofficial) menu choices and prices in just about every WDW restaurant.
For a better idea of Quick Service options, check out
the listing on Walt Disney World.com, under "Where to Eat." You can use this list when searching on the above-mentioned site, too!
Please send me any additional questions you may have about your upcoming trip. I love to help!