Touring North Island

I will be spending six weeks with my family in New Zealand in December/January, but before I join them I will be hiring a car at Auckland airport and touring North Island for a week. At the moment, my itinerary is Bay of Islands, Coromandel Peninsula (there is some interesting snorkelling to be done - not coral, but lots of plant and fish life), Rotarua, Taupo, Hawkes Bay,Napier and then a day and night in Wellington. I won't be staying in all the towns, obviously, but in New Zealand I have found the journey is the best part.
Any suggestions grateful accepted as I know several of you have visited and/or have family there.
My daughter is going to take me down to Christchurch for a couple of days - she says it is rising like the phoenix and the route from Richmond is very scenic.