New Zealand in 7 days!

So you arrive Auckland and depart Dunedin 7 days later ?

Or, you connect in Auckland thru to Dunedin, and have 7 days from there?

Sorry. I should have clarified.

Flying into Auckland and heading to Dunedin. My friend's daughter is at U of Otago.

We don't have a flight back to Auckland from Dunedin yet, but we leave from Auckland at the end of trip.

Any advice, recommendations, what should we not miss? This may be once in a lifetime trip for me.

Hire a car to in Dunedin and use it to cover Dunedin to Queenstown/Arrowtown/Wanaka and Te Anau/Milford Sound. Fly back to Auckland directly from Queenstown (book asap at Airnz.co.nz or Jetstar.co.nz).

Good advice from Kiwi.
Would only add that the Otago peninsula would make for a very pretty day trip from Dunedin. We enjoyed our visit to the penguin colony out there.
Queenstown is the jewel of the South Island. The whole area is beautiful. The drive south along the lake to Glenorchy is nice, as is a visit to the Deer Park about 20 minutes out of the city - lots of familiar LOTR film locations up there too, if you're a fan.
Suggest an overnight stay in Te Anau (or two) to simplify the drive to Milford Sound...it would be quite a long day if you try it from Queenstown.

Definitely Otago peninsula from Dunedin. 2 nights in te anau to allow a full day to drive to Milford sound do cruise and return (avoid lunchtime cruise as they are packed with day trippers from Queenstown), then time in Queenstown.

If you can make it work, do a flight from Queenstown to Milford Sound with a cruise and a return bus to Queenstown. Long day and a bit spendy, but very worth it. Unfortunately, flights don't go every day due to the weather conditions, but when they go, totally worth it.

There are so many wonderful things to see and do, fit in what you can and don't feel bad if you can't do it all. Oh, and watch "The World's Fastest Indian" for a true NZ story. It's a story that will warm your heart and provide some understanding to a different country.

But best of all, go, and have a wonderful trip!

It would help if OP can tell us his/her interests, such as hiking or other outdoor activities, photography, wildlife viewing, etc.

Thank you for the ecommendations!

We're into sightseeing, outdoor/nature, activities, museums, churches, etc.

I'd skip the North Island almost entirely. We did three weeks in New Zealand two years ago with another couple and all of us much preferred the South Island. Things we liked best: seeing one of the glaciers (Fox, Franz Josef); staying at the chalets at Mount Cook (favorite place! We loved it!), hanging out in Wanaka. Easy to drive!

There is plenty to keep you busy for all 7 days in Dunedin, the Otago Peninsula, and Queenstown or Arrowtown areas. Do rent a car. If you need suggestions for where to stay in Dunedin, we loved this place close to the University:

http://www.bluestonedunedin.co.nz

If you enjoy cycling, look up the Otago rail-trail. We rode a section near the town of Clyde and discovered a great little B and B there.