The minotaur could have adventures such as befriending other supernatural beings and working together to solve mysteries. Or it might have to face off against powerful foes who are afraid of its strength and uniqueness in a modern setting.
The minotaur protagonist might have adventures like fighting against dark magic forces threatening the city or helping humans understand mythical creatures better. It could also be on a quest to find a powerful artifact that can restore balance to the magical and mundane realms.