there's tour , backpacker's van/bus called kiwiexperience goes around I think....
find out info from the hostel, they sometimes provide really cheap backpack style hostel.
where to visit? Auckland? it's a city like Singapore, skycity tower, parnell, missionbay. What you want to see?
Taupo is not bad, you'll go by pass rotorua, seeing the sheep farm,
what exaclty do you want to see, lots of culture stuff, don't expect shopping!