Well, perhaps they would embark on a journey to solve the mystery of a series of strange disappearances in Hogwarts. The crow, with its sharp eyes, could spot clues that others might miss. Harry, with his magic skills, could then investigate further. They might end up unearthing a plot by some dark wizards who are using the disappearances as a distraction for a bigger, more sinister plan.
One possible adventure could be that the crow senses a powerful but evil magical energy in an old, abandoned castle near Hogwarts. Harry, being the curious and brave wizard he is, decides to investigate with his crow familiar. Along the way, they face various challenges like enchanted traps and dark spirits. The crow uses its ability to fly and scout ahead, warning Harry of impending danger, and together they manage to overcome these obstacles and find out that the source of the evil energy is a cursed object left behind by a powerful dark wizard centuries ago.
They could go on adventures in the Forbidden Forest. The crow might help Harry find hidden paths or sense danger from dark creatures. Maybe they'll discover some long - lost magical artifacts together.