In a similar question (היום אנחנו הולכים למסעדה) I answered ״Today we are going to the restaurant" and it was marked wrong. The correct answer said "to a restaurant". Does -ל imply the need for a definite article versus indefinite article, or not? How would you know which was appropriate?
First of all, I would accept "the restaurant" because maybe they ordered a reservation in a certain restaurant earlier and now it is just a reminder, so to my humble opinion you should send a "my answer should be accepted".
Second, by context it is quite (although not absolutely) clear that the cook is going to a certain restaurant because he is the cook. For general We this context is far from clear so an indefinite article would be more proper.
Another way to look at it is the difference between coming and going. When you come somewhere it is usually to a specific place - therefore a definite article. When you go somewhere it is usually more general - therefore, when no context is known, an indefinite article might be more appropriate.