You're not going to want to drive from Queenstown up to Franz Josef and back the same road. It's gorgeous, but it's a loooong drive (especially the portion through Mt. Aspire National Park). I would recommend flying ROT-CHC-HKK instead.

Speaking of Rotorua, I would also not sleep there. The town reeks of sulfur given the geothermal pools. The one night I spent there was one night too long.

Down in Milford Sound, I would recommend looking into doing a 3-night stay at Fjordland Lodge in Te Anau. You will not regret it, and it gives you a good base for doing a number of activities nearby (boats to Doubtful Sound, driving to Milford Sound, hiking the Kepler Track, etc.). Given the amount of time you are centralizing in Queenstown, I would recommend trekking out a little further.