Well are you dining more for the kids or do you want something more else?
If you are dining for the kids, I would choose a character meal. This will also provide options for your picky eater since all the character meals are either buffet or family-style meals with lots of basic kid fare.
If you want to go that route, I would suggest:
BF at Tusker House in AK (Donald and some of the other classic characters)
BF, Lunch, or Dinner at The Crystal Palace in MK (Winnie the Pooh and friends) - My favorite breakfast in Disney!
BF or Dinner at Chef Mickey's at the CR (Mickey and the classics) - although this gets the most mixed reviews on food quality
Dinner at The Garden Grill in Epcot (Chip, Dale, Mickey, Pluto)
BF at Cape May Cafe in the BC (Minnie, Donald, Goofy) - I liked the food a lot here
BF at 'Ohana in the Poly (Lilo, Stitch, Mickey, and Pluto) - I didn't think the food was very good here though.
Breakfast will be cheaper than lunch or dinner at the above places, but I think all of them, even at dinner will keep you just under or right at the $125.
If you do NOT want a character meal, but still want to go somewhere the kids might enjoy, and have the type of kids offerings to appease the picky eater, I would suggest:
50's Prime Time Cafe (HS) Fun antics and old tv clips in a 50's style 'house'
Sci-Fi Dine In (HS) Eat in a car while watching old sci-fi movie clips
Coral Reef (Epcot) View the aquariums while you eat
Sanaa (AKL Kidani) Views of the animals on the savannahs
Whispering Canyon Cafe (WL) Silly antics in a western setting
Rainforest Cafe (AK or DTD) Rainforest decor
T-REX (DTD) Dinosaur/prehistoric decor
For those restaurants, I think it's possible to keep it under $125 but since the menus are a la carte, you could stay under or go over depending on how much food you want to order.
Menus and prices here:
http://allears.net/menu/menus.htm
My personal choices would be Crystal Palace for a character meal or Sanaa for a non-character meal.