We've eaten at (sometimes with kids):
Coral Reef - expensive, but fun with kids - they see the big tank. Didn't think it was worth the money.
Mexico (San Angel Inn) - A lot of people don't like this because the food isn't what you think of when you think Mexico, but we enjoy it. The kids like watching the water. The restaurant is dark and loud.
China (Nine Dragons) we thought it run of the mill Chinese, but its been several years. If your kids will eat Chinese, this might be a good choice.
Morrocco (Marrakesh) we love this restaurant and have been here several times with kids. The chicken kabobs are good for kids - fairly normal, not spiced oddly. Kids also tend to like couscous.
Italy (Alfredos) - we ate here a long time ago without kids. The first time I went it was wonderful. The second time I went was the last. But if your kids are pasta fans, they will do fine here. Its a little crowded for my taste - without having the casual party-ness of San Angel. My mother in law was here recently and enjoyed it, which may mean its time for me to give it a try again.
Japan (Teppenyaki and Tempura Kiku) - Teppenyaki is a lot of fun with kids. Meat and veggies and rice - the meat and veggies stir fried in front of you on a hot grill. Not oddly tasting at all. Tempura is a little odder - my kids eat it, but "tempura" chicken nuggets are a little different than what your kids are used to.
Canada (Le Cellier) - A steak house with good fish and great steak. Our new favorite. Kids did fine. The Chocolate Moose for dessert is not to be missed!
Germany (Biergarten) - a buffet of German food, including sausages that are "just like" hot dogs (my picky daughter ate these in abudance) and chicken. This is a buffet - so unlike the other restaurants where your picky eaters can share if they say "yuck" to everything on the menu (and then get chicken strips later), you will pay for everyone in the party.
Almost all Disney restaurants have kids menus that have nice normal things on them.