Hi Jamie,
Disney has some fantastic quick service dining restaurants, you can see a full list of which ones are participating in the Quick Service Dining Plan
HERE.
Here are my families favourites for each park -
Magic Kingdom - Columbia Harbour House, it serves lovely sandwiches, soups and also has yummy chicken and fish.
Epcot - For the huge variety it has to be Sunshine Seasons in The Land. The choice is extensive from rotisserie chicken to Asian cuisine and the desserts are delicious. Also be sure to sample some of the quick service food on offer around the World Showcase!
Disney's Hollywood Studios - Our favourite here is Starring Rolls Cafe, with it's choice of sandwiches, pastries and fruit it makes a nice change from burgers. Last visit they even had some of the famous Brown Derby Grapefruit Cake for sale.
Disney's Animal Kingdom - Most people love Flame Tree Barbecue but my family loves Pizzafari, especially the chicken caeser salad, yep salad in a pizza place!
I know you only asked for the parks but I couldn't leave out my very favourite which is Earl of Sandwich at Downtown Disney. The hot sandwiches are delicious and I just love their cupcakes.
I hope that helps and you have a fantastic trip,
Jo