A Healthy Lunch for Daycare?

My baby recently started daycare three days a week. (I keep calling him 'baby' all the time even though he will be three years old in four months.)

So I've been making daycare lunches for him for the first time.

I'd like to make healthy lunches but I find it hard to think of good ideas for his lunch container. He's not a 'sandwich' eater yet. When we're at home for lunch I usually reheat leftovers from the previous dinner, or make him some scrambled egg and toast, or open a can of tuna or sardines or salmon and give it to him with healthy crackers. Then there is fruit, yoghurt and basically the entire contents of the fridge and cupboards are open for me to offer him, as he can often be a finicky eater.

But at the daycare they ask that the food does not require refrigeration or heating-up. So that limits it a bit. They also don't allow any kind of nuts which is hard because nuts are so good for him and he can eat a lot of them. I once included a flax granola bar in his lunch but was quickly educated that this is not allowed as it may contain traces of peanut products.

I would love to get some ideas from people as to what they put in their toddler's lunch box. Here's what I've been doing so far;

Yoghurt
I often include a yoghurt in his lunch. I prefer to buy the large (non-premixed) containers and give him an individual serving in a small re-washable plastic container rather than buying the individually portioned cups. It's usually a lot cheaper and much better for the environment.

Fruit
I usually include a piece of fruit, most often a banana, but sometimes grapes or berries (rasberries, strawberries or blueberries as they have been in season). I put the berries in a small plastic container as above.

Sandwich
I often make a cheese sandwich (with a bit of ketchup, as this multiplies the odds of him eating it), cut the rinds off, and cut it into little squares. He often doesn't eat it.

Crackers and Cheese
This is a current food fad with him. A little cracker with a slice of cheese on it.

Leftover Chicken
I often include little pieces of chicken in another plastic container if we happen to have some leftover.

Carrot Sticks
He seems to like finely cut carrot sticks right now.

Heavily Diluted Juice
I give him a sippy cup filled with about 1/4 cranberry juice and 3/4 water.

So, other than the carrot sticks, the vegetable quota in the lunches is almost zero. And it seems I must be missing on some good stuff. I'm thinking there must be more good ideas for what to make. Would love to hear from people about this!