When you say you are going to the cinema, you are referencing a specific place.
When you say you are going to school, you are referencing an event, more than a place.
You may just as equally have said
I am going to cinema (it sounds odd, but replace it with "theatre": "While I'm in New York, I plan on going to theatre and eating out a lot.")
I am going to the school ("I am not at all happy about what happened to my son yesterday, so I am going to the school to talk to the principal about it."
In this case, "theatre" is an event - you aren't mentioning a specific building or even a specific performance - you are just hoping to enjoy a live theatrical experience. And when you go to the school to address the principal, you have a specific destination in mind.
You go to school to get an education; you go to the school when you hear the bell ring.
I hope this helps?
Student or Learner