While Ron did give good guidance, it's really not done this meticulously in practice though it sounds good in theory.  In practice, there seems to be overlap between the two and there is no official rule specifying a time frame when you have to switch from one to another. Every French speaker seems to decide for themselves. If the action is not pretty much immediate (like screaming "I'm coming!" as you run towards the ringing doorbell) but within 24 hours, both the future proche and the present seem acceptable.

Of course there is a subtle difference. 

Demain, il arrive à dix heures.---Tomorrow's he's arriving at ten o'clock.

Demain, il va arriver à dix heures.--Tomorrow, he will arrive at ten o'clock. 

They are both valid in English and they are both valid in French. 

Also, I actually don't think that you can say  "Je vais partir d'ici deux heures". Do you mean "Je vais partir d'ici à deux heures?" (at two o'clock)

I think your answer would also be valid, but the English version you're asked to translate is: "You are going to buy a new car tomorrow" which hints that you should use the futur proche. If it had been "You're buying a new car tomorrow" then your answer would be correct.