Individual yogurts are pretty portable and kid-friendly.
I frequently eat out of a cooler of food from home when I travel for work. I kind of make it a game to try to not go out to eat at all, or only go out once in a week-long trip or whatever. You're at a big advantage having access to a full kitchen each day.
I really like what I think of as "dense" salads to break of the monotony of sandwiches. I just did an overnight trip this week, so I mixed a can of lentils, a can of olives and a can of tuna with some parsley, green onion, bell pepper, vinegar and olive oil, then split that into two portions and ate it as my main meal both days (hotel room had a fridge). Also, hardboiled eggs should travel well and are nutritious, cheap and filling. You can pre-peel them to make it easier to eat while you're out. Carrots, celery and broccoli all do fine outside of refrigeration and don't bruise easily, so they're a good choice. Oranges are good, and apples or grapes if you can prevent them from getting bruised or squashed. I also eat avocados frequently when I'm traveling because they're healthy and filling, and can stand in for dips and dressings. Also, homemade trail mix is great - you can do this on the road by finding a grocery with a bulk section and just buying a little of different nuts and dried fruits, then throwing them all in a bag. Obviously, you could just buy the trail mix as well, I just like choosing my own ingredients and getting a premo mix.