This not planned to make the best use of your time, the itinerary should be Auckland, Tauranga, Napier, Auckland. You don't seem to have studied a map at all and not only will you be a danger on the road with tiredness you will be too exhausted to enjoy anything with this plan. I would leave out Waiheke Island and also leave out Bay of Islands, there is not much there except activities for boaties. A tighter more manageable itinerary would be, Auckland to Tauranga and over to Mt Maunganui for coastal scenery, on to Rotorua and then thru Taupo to Napier. Our roads are not dual carriageways as in other countries, they are windy and need lots of concentration. Try doing a google search for itineraries from the Automobile Association and work out the distances and driving times. There isn't anything of interest for tourists in Tauranga, you could use the bypass when you arrive at the beginning of the city and go to Mt Maunganui which is a very nice town now and the beach is lovely. Once you pick out your stops google each one and then pick out what you want to do while there. Bay of Islands is a long drive from Auckland over many hills let alone from anywhere else.