When flying into Christchurch, hire a car and do a driving itinerary of the South Island. This will allow you to spend some time in the city itself and then trek further beyond, trailing the Pacific Ocean as you go.
Hobbiton is one of the world’s only preserved film sets. Upon arrival, you’ll notice that the site actually looks like people live there. The set is maintained for the tour groups that arrive en mass and even if you’re not a fan, I guarantee you will be impressed.