This article will help you to locate all the in the sidequest “Gobs of Gobstones”. The quest can be initiated by an (NPC) Zenobia Noke in The Astronomy Wing within the castle.
She’ll tell that everyone hates her for no reason and everyone who lost to her in the game of ‘Gobstones’ has taken her Gobstones and hidden them throughout the school. She will ask you to help her to find all of her missing stones. There are six Gobstones missing which are spread over the various castle wings in Hogwarts.
The first stone can be found on top of the walkway right outside the courtyard where you initiated the quest. Go downstairs and into the courtyard and look up the walkway. You’ll need to use Accio to grab the stone.
Follow the quest marker to reach the Divination Classroom. Go upstairs and pass through the door near the fast travel point. The stone can be found resting on some wooden beams near the house flag.
Continue going upstairs from the previous location and before you reach the ladder, look at the chandelier to find the third stone. Use Accio to grab the stone.
Follow the mini-map and it will lead you to the Ravenclaw Tower. After reaching the location, look up at the pillars to find the fourth stone.
Follow the mini-map to reach the Grand Staircase and go all the way up to the trophy room. The fifth Gobstone can be found in front of the Trophy Room.
The last stone can be found inside the trophy room next to a couple of vases and trophies.