In the MK area, I would recommend like the PP did, Crystal Palace. If you don't want a buffet, the dinner at Liberty Tree Tavern is quite all-American as well. Crystal Palace includes Pooh and his friends, which may be a delight for a 5-yr-old.
In the Epcot area, I would recommend Garden Grill (all-you-can-eat steak, turkey, catfish, mac-and-cheese, etc) or, if you wanted something a little nicer, the Captain's Grille at the Beach Club (steaks, crab legs, chops). The Garden Grill includes Chip and Dale and Mickey and Pluto; the Captain's Grille is one of my favorites and includes stellar service and a quiet atmosphere.
In the Studios area, I would recommend 50s Prime Time Cafe. 'Down home' is the very definition of what they offer here - chicken, mashed potatoes, meatloaf, milkshakes.
In the Animal Kingdom area, it is slightly more difficult to find things that are not at least partly exotic in nature. That being said, either the buffet at Tusker House or the buffet at Boma in the Animal Kingdom Lodge both offer 'plain' choices alongside their more 'ethnic' offerings.
In general, when dealing with larger groups and/or picky eaters, it is probably easier to do buffets where everyone can pick from a multitude of things. The buffets all include a 'kids' area with nuggets or mac-and-cheese or pizza, and adults can eat these things too.
If one or more of your 'picky' folks is an adult, be aware that in most cases a table service restaurant will serve an adult a portion of a kids' meal entree - chicken nuggets, for example - but it will be a larger portion at adult-level prices. I had a friend who is a terribly picky eater go with us a couple of years ago, and she had chicken nuggets a couple of times while we ate things she refused to try.
HTH
