I have a newly 4 year old and just shy of 2 year old and the three places the 4 year old will tell people are her favorite places to eat are:
Goofy's Kitchen-if we go we do it the night we arrive for dinner and try to get like a 5 or 5:15 reservation so the kids can still get to bed at a normal time since we want to be ready to hit the parks the next day
Brunch at Lamplight Lounge-this one you have to be on right at 6 AM to get since it is super popular and only offered Friday-Sundays. If I can get this one I like to try and get like at 10:30 reservation so afterwards we can do a ride or 2 and then head back for naps. My kids like the breakfast quesadilla and the omelet. Both come with fruit on the side though it is usually strawberries (which my kids like) but some of the adult food comes with watermelon so I always order my kids a side of watermelon also otherwise they steal my watermelon. I like the flautas (but they are spicy) or the chiliquelies (they are huge and potentially shareable).
Her other favorite is actually Carthay Circle Lounge. They have a shells with marinara on the kids menu that can be ordered with just butter instead and she tells people it is the best butter pasta in the whole world. Comes with orange slices and grapes usually which is fine for my 4 year old but I still have to cut up the grapes for my little one which is a little bit of a pain but they both inhale the pasta. Nice thing about Carthay Circle Lounge is it opens at 11 as opposed to 11:30 which just works better for my family since right after lunch we usually go back to nap. This menu changes a bit every few months but almost everything I have ever had there has been good.
We tend to eat bigger lunches (at places with reservations) and snack or eat quick service for dinner.