Car hire is a lot cheaper. I would suggest doing the South island, but depends where you fly into. If its Auckland then train down to wellington, and do the ferry trip down to the top of the South island where you can hire a car (or hire it in wellington and take it down on the ferry).
Heaps of stuff to do on the South island, but make sure you hit Hamner Springs on your way through, and the Glaciers on the west coast, and Queenstown too. Heaps of stuff to do at all those, especially Queenstows where depending on the season has some of the best skiing you can get.
Oh if you like wine then you HAVE to hit Malborough and Blenheim ... the later has some of the best Sav Blaunc in the world.