One week is not much for Aotearoa(The Land of the Long White Cloud). (Yes, we tend to use a lot of Maori words when we speak, it's second nature to us.).
I would spend a day in and around Auckland, also I'd go up north of Auckland about half an hour away is the Hibiscus Coast. There's a town called Orewa and a peninsula called Whangaparaoa. It's a nice area, I used to live there myself for a few years.
Now I live more out in the country, a town on the rodeo circuit!(You can imagine)
Also, from Auckland city she can hop on a boat to either Waiheke Island(if i remember correctly about half an hour away) or to the Great Barrier Island(I can't remember how long it takes to get there, maybe a couple hours atleast by boat).
I've been to Waiheke, it's pretty nice, although the people are a bit screwy.
To be honest I'd then go straight down to the South Island.
Queenstown! Visit Mount Cook!
Franz Josef glacier.
The Southern Alps are awesome.
Also down there is the Fiordland National Park. Haven't been there yet, but I'm dying to.(If only I had some time.)
Oh yeah, and if some Kiwi wanker tells her that the South Island has a different monetary system than the North Island and he just so happens to be an official exchange office, tell your daughter not to fall for it! Yes, it happened. And yes, I laughed my ass off for hours when I found out.
If she doesn't have time to go down to the South Island, she can visit Mt. Egmont, near New Plymouth. Also called Mt. Taranaki (in Maori). I've been there, the national park and the town are both very cool.
Also, she can visit the Waitomo Caves, just north of the town Te Kuiti.(been there, I liked it)
Taupo, on the edge of Lake Taupo is also VERY nice.(Been there a million times, I love it, I'd love to live there.)
Then ofcourse there's the Tongariro National Park just south of lake taupo. There you will find the active volcano named Mt. Ruapehu. Lot's to visit there if you like mountains, and skiing. I'm not sure if it's still skiing season. If it still is, it'll be over soon though for sure. It's just become Spring here. But there's plenty to see and do there even without skiing.
Also Rotorua is nice (gaisers, hot springs and maori culture). Slightly too touristy. We often call it Roto-vegas.
Lastly for the North island I would suggest visiting Mt. Maunganui(a beach town) and also the Coromandel Peninsula.
Tell her to have fun, and STAY SAFE.
NZ is not as safe as some foreigners seem to like to imagine. Criminals(as can be fully expected) take full advantage of the communist gun laws in place here(unarmed citizens produce armed criminals).
