Hamburgers are generally awful, not that there is anything wrong with the meat but they have not mastered the ketchup thing yet. Keftedes are little fried meatballs and they are usually a big hit. Chicken tastes like chicken anywhere only better and it's the least expensive meat on the menu. It comes with roast or fried potatoes. Get them to try the roasted ones first and if they don't like them switch to fries.
French fries are amazing.
Kids love them and in many places they are cooked in olive oil so you can enjoy them too. In places like Lesvos where fish are cheap you can get marides which are tiny deep fried fish that can be eaten whole. My daughter loves them and yours may too. Reward Systems for Good behavior Ice-cream is a key ingredient for a successful vacation. You will see a brightly colored freezer box with doors on the top and large colored posters of each variety, expertly made to capture the attention of kids from any country.