Auckland's pretty dull. Get up early, head up to Paihia for a couple of nights. If you time it right, stop in at Matakana on the way up on market day. Nice little posh arty/crafty market. Good for a wander round. From Paihia get the ferry over to Russell for an afternoon, lovely little town. Do a boat trip or kayak trip in the Bay of Islands. Back to Auckland on SH16 via the Kauri forests (what's left of them) on the west coast, including the Kauri museum.
Then I'd head to Rotorua, a 3-4hr drive. Te Puia is good, it's pricey but you get to see some good geothermal activity and some 'authentic' Maori experiences. It's cheesy but quite good if you've never seen anythign of that sort before. They also have a school on site where people train in traditional Maori carving (wood, pounamu, stone) weaving etc. and you can watch them. Quite interesting. Waimangu Valley is also good, but also pricey. You could always just wander through Kuirau Park in the town, it's free and they have lots of bubbling mud pools Image may be NSFW.
Clik here to view.
From there head down to National Park for a couple of nights to do the Tongariro Crossing. All the accommodation providers can set you up with transport to and from the start/end points. It's a long-ish but non-technical walk. Need to be prepared for changeable weather up top, it's very exposed. It's absolutely stunning though, I've done it twice and rate it as one of the best trips I've done in 7.5 years here.
If Tongariro is too far, try the Pinnacles walk from Thames (on the Coromandel). Hot Water Beach is good too, all you do is sit in a puddle on the beach with a bunch of strangers, but is worth a visit for the novelty value.
