I am travelling in New Zealand this year and about to embark upon my journey through the South Island hopefully stopping in Queenstown for a while and looking for the must see's and do's.
Mount Cook (and the drive there) Lake Tekapo, the lake at Twizel, Queenstown, Wanaka, Arthur's Pass, Haas Pass, Milford Sound. The treks are sublime, if you like doing that. If that's not your thing you can still do a day-walk from Glenorchy to Routeburn Flats. If ou like trekking, look at http://www.doc.govt.nz/parks-and-recreation/tracks-and-walks/fiordland/ about 5 years ago
Milford Sound (although the tunnel closed yesterday for 2 weeks so only ingress is by air and hostel closed during this time too), Drive Te Anau to Queenstown, Lake Tekapo and the hot spring baths there. If you have a car, there are many beautiful drives and the DOC (Dept of Conservation) signposts places of interest along the way. Mt Cook is great but I hear even better by helicopter. On the East Coast the Otago Peninsular drive. Queenstown good for activites about 5 years ago