Definitely worth it.
I don't remember internal flights being all too expensive (though that may of changed in the past few years). I flew to Auckland and then got an internal flight to Wellington as it was the quickest and cheapest route.
I knew someone who owned a car yard over there so he gave us(me and DP) a car to use the whole time we were there so we could just hop on the state highways. I'm not too sure what the transport links further a field are like to be honest. In and around Wellington the buses and trains are good. The ferry is a good way of getting from the north island to the south.
I'd definitely recommend getting over to Oz though if you can, even if just for a week here and there. That's the one thing I wish we'd have done.
The bay of islands is a must if you're into water sports. Scuba diving, sailing, fishing, whale watching etc.
Waiheke Island or Martinborough if you're into wine. Lots of lovely vineyards. We went on a bike ride and get ver ver drunk 
White Island (active volcano) - you can take a helicopter ride - absolutely amazing!! Stinks a bit though lol. Lake Taupo, Tongariro nation park and Rotarua are volcanoey places which are lovely and stinky too! Went horse riding up a mountain in Rotarua - the views were magnificent!! Forgot our camera though didn't we 
Queenstown - good of you're an adrenaline junkie, skydiving, skiing, bungee jumping, jet skis, rafting, cliff jumping etc. I was too chicken to do most of it though haha.
Franz Josef glacier - again, helicopter ride, ice climbing, hot pools. There's loads more lovely similar places, particularly in the South Island! Milford Sound is meant to be beautiful too but we didn't get chance to go.
Cape Pallisar - about 2 hours from Wellington, loads of seals chilling on the rocks there! If you climb to the top where there's a lighthouse the view is glorious!!
Mount maunganui is one of the best beaches in nz! Climb to the top of the mountain, the views are amazing, you won't be disappointed!
There's a little town I can't remember the name of it, hobbit something I think, but if you're into lord of the rings then go! It's a replica of the shire. There are tours around Wellington also where they filmed a lot of it.
There's so much more to do, any of the hundreds of national parks are good places to go. Please research and just go everywhere you get the chance!
You're making me want to go back and do it all again 

