The key is to get them interested in souvlaki because then life becomes a breeze. You can sit down to a quiet dinner and send them next door on their own to buy a souvlaki like it's a big cultural adventure. When we were kids that's all we ate. 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.