For the airplane, plenty of snacks and lolipops, a magnadoodle, portable DVD player. I usually just put a few crayons/pens in a ziploc and have a small 4x6 size notepad to write on, and 1 colorbook. Both my sons will carry a small backpack that they can fill with little toys and action figures. I also bring tissues, wetwipes, sanitizer, and 1 change of underwear.
At a restaurant, they are allowed to bring in ONLY 2 actionfigures. Usually the servers bring a paper and crayons to color.