Hi Luke,
Lucky you! NZ is my favourite place and a month is nowhere near long enough!
Still, from Auckland, Rotorua is a must for its thermal activity.
Lake Taupo nearby might be worth a stop. If you go towards Waitomo (middle of the North Island), stay at Te Tiro cabins (look in guide books or ask at TI centre). The Tongariro National Park contains Mt Ruapehi - or Mt Doom from LOTR. It's mighty impressive, looking for all the world like Kilimanjaro, except you can just drive right by it!
Wellington gets good reviews, but I missed out myself.
The South island is heaven. You could spend a month here. The NE is wine country. Down the E coast is Kaikoura where you can go whale spotting.
Franz Josef Glacier is on the west, as is the spectacular Milford Sound, further South - stay at Te Anua not far away.
Dunedin is a nice town (SE) and there are loads of others dotted about. Christchurch is in the Canterbury Plains - totally flat, by way of contrast with most of the rest of the place.
I recommend some sort of Maori experience. We went to Waitangi where the treaty was signed in 1859. Our warrior showed us around and took us to the Marae. It was a spiritual experience. Highly recommended.
Waitangi is in the Bay of Islands which, unfortunately is North of Auckland.
Car hire is reasonable - you can get a 'rent a dent' as well as all the big companies.
But by far the best way is to hire a motorhome. Not cheap, but well worth it if you're travelling regularly, as it save you looking around for places to stay all the time.