We went last year on the dining plan with a 3 year old son and an 8 month old son. We did the Crystal Palace, and we loved it. The characters kept the boys so distracted that we were all able to eat an enjoyable. meal. We also did the O'Hana breakfast with Lilo, Stitch, Mickey, and Pluto, and our boys absolutely loved it. We had no complaints there either. We ate at Tony's Town Square in the Magic Kingdom. We enjoyed the meal. It is a loud restaurant, but that helped mask my 3 year old being loud too.
We are going to be there during free dining this time too, and we will also be at CBR. This time we are going to Teppan Edo because we think the boys will enjoy the food and the preparation show. I think for us it was important to balance eating at character meals and more adult styled meals. We had a great trip and didn't have a bad meal the whole trip.
As for counter service places, we enjoyed Pizza Planet (DHS), Pecos Bill (MK), Pizzafari (AK), and Pinnochio's Village Haus (MK).
When will you be at WDW? We will be there September 20-25.