Good on ya for wanting to take a leisurely approach, but this itinerary is not what I'd consider leisurely!

A few comments...

I'd not stay overnight in Greymouth, but keep moving. If you leave Christchurch early in the day, you can easily drive over the pass, make the detour to Punakaiki (Pancake Rocks)
and still get to the glaciers in good time. I always recommend at least two nights at the glaciers, which will allow one full day to hike, take a helihike, etc and leave enough time if an activity is cancelled due to bad weather, which is often the case on the West Coast.

Greymouth to Wanaka with a stop at the glaciers is not what I consider leisurely - it's close to a seven hour drive w/o stops and there are many reasons to stop.

How much time you allow in QT depends on what you want to do, but we've found that 3-5 nights has worked well for us in the past. We don't care for QT so much anymore so in recent years we've based ourselves in Arrowtown, which is a short drive from the attractions of QT w/o having to stay in the thick of things.

I suggest spending that second night in Te Anau, which will make your drive to Dunedin or Mt Cook shorter the following day.

Te Anau to Dunedin is a 4 hour drive, Te Anau to Mt Cook is over a six hour drive. If you go to Dunedin, do you plan to fly back to Christchurch?

How many nights total in NZ are we looking at? I can be of more help if I have the exact number.

Melnq8, thank you so much for your thoughtful response. We have a total of 14 days to enjoy the South Island. As mentioned above, we've checked guidebooks, and other forum posts, but grasping the distances in the South Island is difficult. We've revised our itinerary a bit based on your suggestions, and would appreciate your response to these remaining concerns:
If we enjoy the drive over Arthur's Pass with a detour to Punakakai as you suggest, where would be a practical spot to reach to stay overnight? We like your idea of spending two nights in the glacier area.
Where would be a good overnight stop between the glacier area and Queenstown (or Arrowtown)?
We're adding another overnight in Te Anau as you suggest. From there we'll explore Milford Sound. Would you suggest an overnight at Milford Sound? We'd like to book a fjord cruise. We'd prefer not to move locations if time allows us to return to our place in Te Anau.
Is it practical to do a trip to Mt. Cook from Queenstown, perhaps staying overnight in the Mt. Cook area? If so, we'll try to arrange our flight to Auckland from Queenstown. At this point, our flight is "on hold" out of Christchurch. . .but since we realized the length of the drive, we'd like to change that.
Last question: Is it worth it to visit the Dunedin, or other little towns in the area?

Thanks so much for any ideas/suggestions you may have to help us firm up our itinerary.

<If we enjoy the drive over Arthur's Pass with a detour to Punakakai as you suggest, where would be a practical spot to reach to stay overnight? We like your idea of spending two nights in the glacier area.>

I'm suggesting you drive from Christchurch via Arthur's Pass, make the 45 minute detour north to Punakaiki, spend an hour or so, turn around and head to the glaciers via Greymouth and spend that first night in the glaciers. Easy to do if you plan well. Christchurch to Franz Josef is about 395 km about 5.5 hours. The detour to Punakaiki is 45 minute x 2 plus the time you spend there. If this is too much driving for you, you might consider an overnight in Hokitika.

<Where would be a good overnight stop between the glacier area and Queenstown (or Arrowtown)?>

Wanaka. Or if you want to explore the wine region, Cromwell, athough it's not exactly a tourist mecca.

<Would you suggest an overnight at Milford Sound?>

Not really. Not much there, limited food options, etc. A return to Te Anau for the night would be my suggestion.

<Is it practical to do a trip to Mt. Cook from Queenstown, perhaps staying overnight in the Mt. Cook area??

By the time you reach MT Cook, you might as well spend the night and then continue driving back to Christchurch for departure. Mt Cook is about mid-way between QT and Christchurch, so bactracking doesn't really make sense.

Dunedin...I'm not a fan, but other like it. It's a city, not what I go to NZ for. IMO it's not worth inserting into an itinerary if time is short.

Lots of other places to visit, but I've got to get to the dentist. Will check back later.

Okay...

14 days means 13 nights

You could do something like this:

Arrive Christchurch, overnight

Drive Christchurch via Arthur's Pass - detour to Punakaiki - overnight Punakaiki (4:20 drive from Christchurch) or overnight Greymouth (about a five hour drive, including side trip to Punakaiki and back) or overnight in Hokitika (35 minutes further from Greymouth).

Drive from whichever above to glaciers for two nights

Drive from glaciers to Wanaka for two nights (4 hour drive)

Drive from Wanaka to Te Anau for two nights (4 hour drive - visit Milford from Te Anau - two hour drive from Te Anau)

Drive from Te Anau to QT/Arrowtown - three nights

Drive from Qt/Arrowtown to Mt Cook - one night (4:45 hour dirve)

Drive from Mt Cook to Christchurch - one night before flight

This route involves plenty of driving, but it covers some of the most popular attractions and some gorgeous scenery.

If you'd rather fly Christchurch to QT or Dunedin and only drive one way, you'd have to choose between the West Coast route (glaciers) and the inland route (Mt Cook), but you'd have less driving and more time to relax. It really comes down to your personal traveling style.

Again, many thanks melnq8 for your great ideas. We think we'll go for your suggested itinerary which allows us to experience more of the beauty of the South Island, albeit less leisurely. At least we will be able to spend two/three nights at some destinations. After traveling so far (from the US) we'd like to enjoy as much of the variety of gorgeous scenery as possible.

We especially appreciate your indication of places to overnight. We neglected to mention that we'll be in the South Island in mid-late February. Do you think we'd have to book ahead on all lodging? We'd like to book the busier areas, like Queenstown, Te Anau?, and locations where lodging is limited. But it's nice to have some open days to "play it by ear". We'd value your opinion on this.

February is high season, but NZ school holidays will be over then (estimated return to school is Jan 30-Feb 7 last I heard).

It's best to book in small areas with limited accommodation - Mt Cook, both glaciers, Punakaiki if you stay there. Te Anau has more accommmodation than you'd think and in my experience, the vast majority of visitors to Milford don't stay in Te Anau, they drive in/out from QT. It never hurts to book though, especially if you're fussed about accommodation.

I've never ever booked the Milford Cruise. I just turn up. You'll probably be okay booking just a day ahead if at all. Doubtful is a different story - you'll want to book in advance. You'll probably want to book a helihike or guided glacier hike a few days in advance too, but you might wait to see what the weather has in store.

My advice - book anything you absolutely don't want to miss out on or any specific accommodation you've got your heart set on.

Good guidelines. They really give us some direction. We like your idea of watching the weather. . .booking a day or two in advance for the helihike in the glacier area. It sounds as if places like Te Anau might give us a little wiggle room on overnight decisions. And waiting to book the Milford Cruise is also an idea which fits or style. Again, thanks so much Melnq8, for your thoughtful responses, both here and on our other post regarding Christchurch.