Well you certainly have stirred the pot, pun intended, with this thread! One thing you have that my family doesn't (now), are young children, who can be picky eaters and I've witnessed dinners ruined over it. We have over thirty years experience , including raising a girl who has been with us in the park(s) since she was 3 yrs old, so for what its worth, my recommendations:
Inside
Disneyland: Cafe Orleans (Pomme frittes, French Onion Soup, 3 Cheese Monte Cristo) and Carnation Cafe (Chili)...we have done BB, but like the ambiance more than the service or the food (my own opinion, of course).
Inside DCA: Carthay Circle, even though it is expensive for 4, the food is amazing and a little culture never hurts anyone.
DTD and Resorts: Our must have is Steakhouse 55, again expensive, but we are foodies and the wife loves her lobster. They have a great menu for the kids too. Catal in DTD hase nice food as well.
On a budget? We are, except for dinner (couldn't you guess?), but if we can't have the aforementioned, then dining with or without reservations at Riverbelle Terrace is a nice option now in DL, and the Plaza has okay quick service with inside dining, if you can get it. At DCA we like Flo's V8 Cafe and the Mediterranean Garden up on the Boardwalk, for salads, pasta, flatbreads, etc.
Hope this helps.