I'm looking for a game where everything that happens is down to the player, rather than a visual novel type game where everything happens in sort of a linear way.
Is there anything like this? Preferably with a school setting.
Glassix is a great example. It still has a story, but after introduction it will be complete sandbox. You can go wherever you like and do whatever you like. There is a lot of characters, so you can even choose who to date. And yes, you are a student, so you can go to school and date your classmates, teacher, principal or other teachers or students from other class.