In my experience as a care provider, the best offerings for a child's lunch are ones that need very little adult assistance. (teachers are too busy, really, to be heating things up, even if it's only a hot dog or mac-n-cheese. Use the thermos for hot food.) Here are things that certainly will pass muster, and that children/their teachers commonly like:
Hard-boiled eggs- peel them, place in a container prepped (does your kid hate yolks? remove them!)and ready to eat.
String cheese or cheese slices- we don't mind opening these for the kids. Good protein and not too messy; they are usually guaranteed to be eaten.
Tamari or plain almonds- unless your care center is a no-nut zone, these are also a bit hit with kids.
Cream cheese or peanut butter and jam on graham crackers- a slight twist on the sandwich, a big favorite with kids.
Whole grain crackers
Hummus to go with crackers or carrot sticks or red pepper slices.
Rice cakes--some kids love them, some, not so much.
Hot thermos-- last night's leftovers go great in here: spaghetti/pasta, couscous and veggies, or stews are wonderful on cooler days. Just fill thermos with boiling water for five minutes or so to heat up before adding hot food. Be sure to pack a utensil.
Applesauce cups or small yogurt cups. If they don't have a lid, transfer them to a container from home that does, or you'll have a big mess later on.
Turkey wraps with cream cheese inside. Just lay out a couple pieces of sliced turkey/tofurkey, smear cream cheese on it and roll it up. Or use a small flour tortilla if you want it to be more substantial.
Dried fruit bars like Cliff's "Nectar" bars or the Lara bars. Other bars offer too much sugar and chocolate, and kids do tend to crash from them. These, from what I've seen, are just plain dried fruit and nuts and have a lower glycemic index: their blood sugar will be more regulated, resulting in less stress for all later on.
Hope this gives you a few ideas that work for you!