Well, there are a number of addtional details that would be helpful in giving you good advice. First, are the kids picky eaters and second are you on a restricted budget.
My initial reaction was the the Electric Umbrella is always a safe bet, and it you do any of the countries, they all have "American" kids menu offerings, although they can get repetitive after a while. Also you have sit down restaurants at most countries as well as a "casual" pick up spot. For example, the mexican restaurant San Angel, the inside restaurant has classic Mexican entree's, but the kids menu, like the Cafe outside is taco's, enchilada's and the like.
So with childrens menu's, you can choose most anywhere to your taste, and have "safe" children's alternatives available.
If the children do like different foods, China is well, Chinese food, Japan has a
Teppanyaki grill that many enjoy, and nothing too spicy, UK always has fish and chips to fall back on that is a little different from burgers and chicken strips.
Attached is a link to my favorite food site so you can easily compare what is available:
http://www.allearsnet.com/menu/menus.htm#epc