I've done plenty of travelling internationally with my kids, currently 2 and 5. My wife is a tyrant about the kids eating, and the kids are a bit picky when faced with unfamiliar foods. The solution was to find rooms that had kitchens. Last year we stayed in Da Nang, Vietnam athe the Fusion Suites. It was awesome, big rooms under $100 with kitchenettes. My wife cooked breakfast, we would go out all day and have lunch outside, and we were usually home for dinner. She would cook while I would hit a local stand and pick up a seafood feast each night for dinner for the adults. If you're concerned about lunch for your child, you could always cook a lunch or prepare a picnic.