That is way too much driving; you're on the road nearly every day.
For two weeks, and if you must go to the North Island for the Bay of Islands, I would do something like 10-11 days in the south and 3-4 days in the north. In the south, pick 3 areas and explorer around those; the closer the better. I don't have much to say about the north as I only visited Auckland, though do the Coast-to-Coast Walk; you get to see a bit of the city that way and it's only 10 miles one way.