We did NZ earlier in the year & our S Island highlights/reccomendations are -
(At least 1/2 day) mtb in queenstown - awesome uplift, views, people & trails all followed by a Fergburger
Milford Sound - journey there from Queenstown is amazing & worth it by
Wanaka is beautiful & as above well worth a 1/2 day mtb hire
Drive up the W Coast - its an amazing & unique ecosystem/geology & one of the best coastal trips we did in a 6 month world travel
A Helihike on the Fox Glacier - helicopters + glacier = win.
Kayaking in the Abel Tasman - more beautiful coastline but no cars allowed
Swimming with dolphins in Kaikora - we were surrounded by 600+ dolphins all wanting to play if you are. Huge smiles all round & quite possible the best thing we did in NZ
Lots there & way more than 6 days worth (we were there for c4 weeks). One of the main things we enjoyed was driving (we borrowed a friends campervan) from place to place, parking up at night & waking in the morning to amazing vistas, sites & visitors (seals, pukekos, keas).
As mentioned above the distances are quite large & although very doable (especially having driven in oz & you like driving) the roads in places are either A roads & you'll find yourself stuck behind campers or very very twist and turny (v different to roads in US or Oz) and you can't actually go that fast so it'll take you ages to get there (iirc there was one stretch of road with bends on it that had a 10 km/h limit).