We drove about 4,000k there in about 3 weeks. Main thing I would say is make sure you take the time to stop at the roadside pull-ins. You can get some fantastic views and shots - so keep your camera charged!
Not sure if you have anything like the 3 mobile deal we do in the UK but it gave us free data while in NZ so I just took a dashboard holder and used google maps for the whole time was perfectly fine. Do keep a paper map just in case you totally lose signal and get lost - but given there are so few roads its generally pretty easy to find your way or just ask someone. You can get a decent enough free one in the i-site's if you dont get one with the hire car.
Apart from that driving was pretty easy, try not to get too frustrated when you get stuck behind a camper van, otherwise you may end up trying to overtake in an unsafe area.