Two ideas:

1. Small backpack with laptop back pocket and large vertical zip front pocket: a) Rangeland Travel backpack, or b) Tucano Tugo. Both bags have large, vertical zip front pockets that can hold a 32oz water bottle and a separate back pocket that can hold a 15" laptop. The Rangeland is the least expensive but it doesn't have the most confidence inspiring zippers and its boxy shape is not exactly fashionable. The Tucano Tugo has beefy zippers but the storm flap over the main zipper makes it hard to use and its book style opening is less preferable than a bag that opens from top to bottom. Both bags are actually more travel oriented than EDC.
2. Small backpack with laptop back pocket and separate zippered side pockets: a) Jansport Field Pack, or b) Datsusara Field Pack 16L. I don't own either of these two packs so I can't speak to each one's functionality. Jansport quality can be hit or miss. The Datsusara is the most expensive of these four and may not be worth purchasing if your child buys a new bag every year.