Points of interest I'd suggest:
Coromandel peninsula. Plenty of white sand beaches and picturesque views. There is a beach called hot water beach, you should aim to visit on a day where low tide is in the afternoon.
Forgotten worlds highway from Taumarunui to new Plymouth, great fun motorbike road and scenery that NZ is famous for.
Rotorua is a great place to blow a bit of money, luge riding, zorbing, sky swings and geothermal hotpools/mudbaths etc.
Lake Taupo is a nice tourist destination, go to De Brets hot pools.
The south island has a lot more amazing scenery, tourist destinations and fun roads for motorbikes.
Personally I'd aim to spend at least 2 weeks in the south island. Do a loop of the south island, off the ferry go through nelson down the west coast, look at the glaciers etc. Then across to Queenstown, Christchurch and up the east coast through kaikoura. South islanders would be able to give you a better idea of where to go and what to see.
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