Soo much to see. On north island: Waitomo caves with glow worms, Rotorua and Taupo with all the thermal hot pool stuff (search for 'kerosene creek") and Maori cultural experience. Napier (of course I live there) art deco capital, wineries and nice cycling. Also an out of this world experience is the Tongariro crossing: walking on a sleeping vulcano in a moon landscape. O yes, hot water beach is also an special experience.
And on the south island so many things.
But be carefull on the sometimes very windy roads. And keep driving left....

Also the gannet colony and Te Mata peak near Napier are well worth a visit.