Our kids are now 13, 11, & 3, but we've been going to WDW since the older two were 3 & 5.
Following are our "must do" restaurants & the restaurants that we keep going back to every year because the kids love them:
Chef Mickey's - The only character meal w/ all 5 of the Fab 5 characters (Mickey, Minnie, Goofy, Donald, & Pluto); it's a buffet. It's located in the Contemporary & feels very "Disney-ish" to me w/ the monorail running through. We do the breakfast.
Cinderella's Royal Table (MK) - Character meal w/ the princesses in the castle; you order from a menu. We've done breakfast, lunch, & dinner, but, in the last couple of trips, it's become our traditional "first night in MK" dinner. When our younger DS was 2, he was considered "free", & our server at CRT was absolutely wonderful - the best service & the kindest attention out of all the restaurants where we dined that year!
Crystal Palace (MK) - Character meal w/ Pooh & Friends; it's a buffet. We normally do breakfast or lunch.
Garden Grill (EPCOT) - Character meal w/ Mickey, Pluto, Chip, & Dale; the food is served family-style. It always tastes fresh to me, &, according to the servers, some of the food is grown right there in The Land. The character interaction is always really good, & my kids love how the restaurant slowly revolves through scenes from "Living w/ the Land"
'Ohana (Poly) - There is a character breakfast here, but we do the dinner. The food is served family-style, & there is fun stuff for the kids - coconut races, hula lessons, etc. Plus, the Poly is a lovely resort, & some of the tables have views of the Castle.
Sci-Fi (DHS) - non-character meal; you order from a menu. Our kids really enjoy sitting in the cars & watching the old sci-fi clips!
3 more of our favorites (but not every trip restaurants) are Tony's Town Square (MK), T-Rex Café (DTD), & Whispering Canyon Café (WL) - our kids LOVE Whispering Canyon Café! It's a cowboy/western themed restaurant w/ lots of fun antics.
We also enjoy lunch at Liberty Tree Tavern in the MK.
We also always schedule a Fantasmic Package at Mama Melrose's, try a new World Showcase restaurant each trip, & either go to Yak & Yeti (AK) or Boma (AKL) after our day at the Animal Kingdom.
And, we're trying Be our Guest for the 1st time this year!
Your kids might also enjoy Coral Reef - our kids like sitting by the aquarium & watching the fish. However, last time we were there, we weren't impressed w/ either the food or the service.
Hope this helps some!