Say what you will about the quest for the MacGuffin, it does keep the characters focused and not needing random things to do to fill up time. If, on the other hand, they are studying at school, they aren't going spend every hour at it. Their hobbies will fill time and give them a situation to interact with each other and develop the world-bulding and quite possibly foreshadow things.
So what hobbies do they have? Magical or not? I think I can rule out sleight of hand, which is unimpressive in a world where children can do the spellwork.
Playing cards. Reading novels. One of them definitely goes for long walks. Another one probably bakes.
Hmmm. . . I think one has a puzzle he was given as a child. The thing is that every time you solve it, you can reset it and it will produce a new puzzle. At the moment, he tells stories about the legend that if you solve them all, you find the secret of the universe, which he doubts -- unless the secret of the universe is that wizards are incapable of producing an infinite series of puzzles.