"She is at the farm."
Translation:Zij is op de boerderij.
As a native English speaker (northeast US) I would always consider "to hospital" wrong.
Sitting here thinking about this it seems to me that the definite article can be/is typically omitted when the subject is participating in the typical activity associated with the location. When you "go to bed" you are expected to be bedding down and sleeping, when you "go to shcool" you are expected to be participating in getting "schooled", and when you "go to church" you are expected to be participating in the service/mass whatever.
I think the difference can be exemplified thus: I went to church yesterday (for the evening mass). I went to the church yesterday (for a community lunch).
I think this is correct. You use the definite article when specifying the location. You don't use it when specifying an activity.
I go to school at the school. However, on Sunday, I go to Sunday school at the church. When my wife is angry with me, I don't go to bed in the bed. I sleep on the couch!