The correct answer to this open question is the following.
The direction that an ancient Mesopotamia travel to get Nineveh from Nuzi is "North."
If we see the map of ancient Mesopotamia, we can see the many powerful city-states it had across the Sumerian territory that was first established between the Tigris and Euphrates Rivers and spread from there to other regions. We can see in the map the important city.states of Nippur, Kish, Lagash, Ur, Uruk, Eridu, and Larsa.
Nuzi was located in the North part of Mesopotamia, close to the Lower Zab River. If people wanted to travel to Nineveh from Nuzi, they had to travel north, crossing Assur and Nimrud. Nineveh was located south Khorsabad.