Hi Mark,
I'd recommend Mt Cook (awesome), Queenstown (beautiful- lunch at Bob's Peak Restaurant, Arrowtown (fascinating), Te Anau (perfect small town), Doubtful Sound over Milford Sound, Gore (if you like fly fishing) Kaikoura (whale watching - spiritual), Nelson (another lovely town - lunch at The Boat Shed) and the drive from Nelson to Picton (along the coast road) is just heavenly. I'd very much recommend that you consider
"multi-modal" transport - i.e mix car hire with train and plane journeys. That will save you valuable time in getting between places and also give you a different perspective of the country. Hope that helps :)