In reply to Caspar: There is plenty of rock climbing in the South Island, in fact you are probably best basing yourself down there if you want both Mountaineering and cragging.
Not sure what conditions you can expect in October, most summer alpine routes are done in the Nov-Feb time, maybe you will be lucky with conditions and weather. Its probably comparable with going to Chamonix in May i.e. late spring. Depends what you want to do...
For mountaineering there are loads of opportunities all down the length of Southern Alps! I suggest getting hold of a few of the NZAC guidebooks. The Mt Cook area has all the big alpine peaks in it such as: Mt Cook, Tasman, Sefton etc.. Be aware that access to some of these climbs can be as hard, if not harder, than the climbs themselves. Also, being only 50-80 km from the Tasman sea, you can expect your climbing windows to be very short, sometimes non-existent, so be flexible and follow the good weather! Many climbers use helicopters to get into the high huts to save time on walking and make best use of good weather.
Another area/peak you might be interested in is Mt Aspiring, a fantastic peak with snow routes at lots of grades and probably a good intro to NZ mountaineering.
If you are into long alpine rock climbs then the Darran mountains in Fiordland is your best bet. I haven't been there much, but Mt Sabre is a fantastic peak in this area.
A good overview of some our best peaks can be found in this book, not really a guide book but gives a taste of NZ mountaineering:
http://www.silverfernz.com/652-classic-peaks-of-new-zealand-book-by-hugh-lo...
As for cragging, well Paynes Ford springs to mind, (Nelson area) but there are plenty of spots to keep you occupied and again the NZAC has a South Island rock climbing guidebook.
http://alpineclub.org.nz/product/south-island-rock
Consider joining the NZAC for discounts on guidebooks and huts and the mountainz forum could be useful for finding partners.
http://mountainz.co.nz/index.php
Hope this helps
Jono