IMO, the most beautiful drives are NOT between Queenstown and Milford Sound. The most beautiful drives during our island circle roadtrip, are

1) between Queenstown to Glenorchy (a dead-end route but well-worth the time and effort for the 4 to 5 hours roundtrip assuming you paused along the way to take in the sceneries and did some minor hiking).

2) the secondary route between Queenstown and Wanaka. this route is a series of serious switch-backs but saves almost hundred kms of driving if you go to West Coast from Queenstown.

3) the secondary route going to Picton (from Nelson). From this route you can see the Queen Charlotte Arm and all the inlets, from the mountain ridge.

4) the northern portion of the West Coast highway.

5) the east coast drive to Kaikoura.

Comparing to the above, the driving between Queenstown, Te Anau, and Milford Sounds, is really, well, no comparison.

The roads in South Island are extremely winding, with countless one-lane bridges but the signages are very very well posted and most cars obeyed the Yield signs. If you ever drove Road to Hana in Maui, then think roads in South Island about as narrow or narrower and more winding, than the Road to Hana. Be prepared for many 180 and 270 degree turns and obey the speed limit guidances - there is not a lot of room to drive safely faster than that being guided. Road surfaces are generally much coarser than you experience in U.S. and for good reason (to increase traction thus safety margin).

The drive thru Arthur Pass is also spectacular (the TranzAlpine route) - we did that in previous trip - and this trip we purposedly did the Island Circle trip - from Christchurch down to Dunedin and started the Southern Scenic Route, to reach Te Anau. Did Milford Sound from Te Anau. Went to Queenstown, and then up Wanaka, and to West Coast. Visited both glaciers, and continued to Abel Tasman National Park. From there headed East to Nelson, then to Picton and then headed down the East Coast, stopped at Kaikoura and backed to Christchurch.