We will be staying at a moderate resort with free dining in Dec. I agree Olivia's is awesome !!! I have stayed there many times but my ex got custody of the points.
Is the mod resort Coronado? At least then you'll have some sit down breakfast options on site.
The Rainforest Cafe by the AK entrance has breakfast. Granted, Rainforest Cafes aren't exclusively Disney, but if you were going to AK, wanted a sit down breakfast but didn't want a character meal, that might be your best bet. Unless you go over to AKL first and have breakfast at Boma.
When you go to MK, the Wave at Contemporary is indeed very good.
@JIMINYCR is right in that they have a buffet, but it's an option, they have regular menu options as well for cooked to order fare. Kona Cafe at Poly is IMO a better option than Grand Floridian Cafe at GF, but your mileage may vary.
On a day you're going to Hollywood Studios, a good option might be the buffet at the Dolphin, if it's available (it's apparently a seasonal offering), or menu offerings at the Swan. Neither restaurant will be on the Dining Plan, but they will take AAA discounts as well as Tables in Wonderland. Captains Grille in Yacht Club, too. Doubt there will be many kids there, they'll all be over at the character breakfast at Beach Club.
Don't know if I'd recommend the haul to Whispering Canyon Cafe for breakfast if you're not staying there. It's fun, but geared for boisterous families, no characters, but continuously loud.
And I'm obsessed with the breakfast pizza at Wolfgang Puck Express, if there's a day you start at Disney Springs. You may have gone before but if you haven't, it's half-a-sit-down meal - you order at the front, you get your own fountain drinks or make your own coffee/tea, but then they bring the food to you and will refresh drinks and check on you. If you're on the dining plan, it counts as a counter service meal, not a table service.
