OK, here's another shot at an itinerary:

Day 1: arrive AUK AM. Wander Viaduct Basin and recover. Sleep in AUK.

Day 2: rent car & drive to Waitomo (2.5 hrs) for GCT (.75 hr), then to Matamata (1.5 hrs) for HMST (2 hrs), then to Rotorua (0.75 hr). Sleep in Rotorua.

Day 3: Rotorua local activities (e.g. zorbing, luge, lake walks, etc.). Sleep in Rotorua.

Day 4: 9:40a flight to CC (arrive 12:25p). Drive to Mt. Cook Village (4 hrs + stops). Sleep in MCV.

Day 5: MCV local activities (e.g. Hooker Valley Track hike; Nat'l Park Visitor Centre; Blue Lakes/Tasman Glacier Viewpoint hike). Sleep in MCV.

Day 6: MCV local activities (Tasman Glacier boat tour). Sleep in MCV.

Day 7: Drive to Wanaka (2.5 hrs) for Puzzling World, Lonely Tree and Roy's Peak Track hike (5-6 hrs) then to QT (1.25 hrs). Sleep in QT.

Day 8: QT local activities (e.g. TSS Earnslaw lake cruise, Gondola/Luge, Queenstown Hill Track, rafting on Shotover River, Ben Lomond Track, Queenstown Trail hiking/biking, horse trekking, Bob's Peak stargazing, Shotover jet rides, guided fishing trip, Highlands Motor Sports Park in Cromwell, visit Arrowtown, visit Glenorchy, etc.). Sleep in QT.

Day 9: Milford Sound day trip (possibly via outbound bus, cruise on sound, and scenic return flight). Sleep in QT.

Day 10: QT local activities. Sleep in QT.

Day 11: QT local activities. Sleep in QT.

Day 12: QT local activities (could potentially do day trip to Oamaru to see penguins and drive back at night, depending on how everyone feels and what we still want to do in QT area). Sleep in QT.

Day 13: QT local activities. Sleep in QT.

Day 14: Fly home (10:55a departure).

Just beginning to look seriously at lodging but am thinking maybe The Hermitage in MCV and the Glebe Apartments in QT.

Feedback?

Can't help with where to leave your luggage while you hike, but if it's all in a concealed trunk, you should be fine.

We do this quite a lot ourselves, but are very careful to not leave anything in sight (and the very reason we never rent a hatchback).

Your itinerary is shaping up nicely - looks good to me.

As for accommodation - The Hermitage in Mt Cook IMO is overrated and overpriced. We much prefer the Aoraki Court.

http://www.aorakicourt.co.nz/

Just a word about food in Mt Cook - in my experience, choices are quite limited, prices high, quality substandard. You might consider self-catering - the Aoraki Court has a full kitchen.

I suggest you pick up supplies en route from Christchurch - Twizel will be your last opportunity before Mt Cook. Geraldine is a possibility depending on your route - Geraldine also has a nice cheese shop (Talbot's) - http://www.talbotforestcheese.co.nz/find-us.php.

Oh yeah, and you can pick up fresh smoked salmon at the Mt Cook Alpine Salmon Farm on the way to Mt Cook as well.

Yes, I agree with you on Aoraki Court but, sadly, it is booked up for our dates. The Hermitage looked like the next best option.

Fresh smoked salmon....you're speaking my language. Will definitely have to grab some of that.

Any particular recommendations for car rental companies? Haven't looked into that at all yet.

Now that's a switch...usually the Hermitage is the first to book up...strictly based on tourist advertising...the word must be out.

For car rental, we like APEX.