Is Auckland on the South IslandAuckland is on the South Island
Since 9 is not enough to discover the two archipelagoes, you should go to Queens Town, where there are many adventures and other outdoor pursuits and you can experience the breathtaking scenery. Or you can go to Wanaka for parachuting. Parachuting in Wanaka is really "WoW"!!!!!! It' s cheaper than the very costly queenstown surgeries - you can still do your river cruise &bungy without having to break the bench.
Bungee would be what I would be saving for Queenstown &rafting maybe in Taupo. You don't have to limit yourself to Queenstown with 9 working nights, although there is a lot to do there. For about 5 workdays in Queenstown and then 1 N in Wanaka; 2 N at Franz Josef Glacier; 1 N Christchurch before I fly back home.
Definately the North Island - as TK says, the Skydive Auckland leap is 16,500FT and at least $45 less than QT's 15,000 feet - an additional 15-20 seconds free fall for less - plus they make a great DVD/Photo pack for only $170 ! Alternative, Taupo, as TK also mentions, is the QT of the North - you can do almost everything in this breathtaking little city on the shores of the sea ("Lake Taupo" is the biggest sea in the south of the hemisphere!) that you can do in QT for a split of the cost.....
Whale-whaling is a little bit hard, but everything from jet-boat riding (Rapids jets are very different from the standard and cheaper), kayaking, parasailing - the fantastic Tongariro National Parks ( Mt DOOM Baby!!!). Our visitors this past season have all said Queenstown is very pricey, overrated and too touristic, and Taupo is so much better.
I' d also imagine flying by chopper to White Island in the Bay of Plenty. New Zealand's adrenaline rush city - Queenstown. Queenstown adrenaline capitol of New Zealand.