Let me preface this by saying that I enjoyed everything I did and saw in New Zealand. With that being said if you have to prioritize I would put a couple of things on the bottom of the list so if you don't get to them, it won't ruin your trip. Also a lot depends on what you (and your travel partners) like.
Winery - if you're totally into New Zealand wines then you could squeeze in a visit just before the ferry to the North Island, otherwise skip it, there are wineries everywhere. Most of the wineries are on the north end of the South Island so convenient for the ferry.
I was in NZ before the Lord of the Rings movies came out so there was no "hobbiton village" but from what I can see it looks like something that kids would enjoy. I don't know about adults unless you're real LOTR fans.
The Rotorua mud pools and geisers were amazing but if you've been to Yellowstone in the US, they are skipable.
It's only a personal opinion but I would put these toward the top of the list:
Wellington, very interesting capitol building, good museums, a ride up the funicular to the top of the hill to the wonderful public flower gardens.
Napier if you're at all interested in Art Deco architecture
We went to the Maori cultural experience at Tamaki, near Rotorua. You could do the geothermal sites during the day and the Maori Hangi (dinner and folklore show) in the evening if you're staying near Rotorua.
Definitely save a full day for Auckland and if you like getting out on the water, take a harbor cruise.
Paihia is a beautiful area and we did the bus tour to Cape Reinga and the 90 mile beach (it's actually not 90 miles long but who's counting it was fun). The bus usually has a race on the beach with another bus so there's some competition there which was fun. We also stopped at some sand dunes that you could slide down on sleds (like snow sledding in bathing suits and shorts).
We didn't get to the Waitomo glow worm caves but it looks interesting.