I agree on Winn-Dixie. You can get a pretty big bucket of chicken wings (many different flavors) from their deli for only $19.99 with their loyalty card. Buy a jar of refrigerated blue cheese and maybe some type of side you can bake and you have a pretty cheap meal that will feed four.You want cheap? Drive over to Wawa and get some nice big subs or some of the many other things on their menu.
A bit further down the street is the Winn-Dixie grocery store, so you can also grab some breakfast stuff or deli items. Eating a few light meals in your room is going to save you the most.
Disney Springs also has some more affordable places to eat, such as the Earl of Sandwich and Chicken Guy.