One of the must do trips on the South Island is Milford Sound. It is only 46 miles west of Queenstown but the road does not go in that direction. The route is 178 miles and takes 3 h and 50 min. Obviously not a direct route.
The boat ride on the Sound is about 2 hours and takes you through the Sound to the Tasman Sea where they turn around and come back. A number of companies offer what seems to be exactly the same excursion The scenery is stunning and if you like waterfalls you will be in heaven. Because of the distance from Queenstown you do not arrive all that early and you cannot leave that late or you will be driving in the dark. If you have a full tank of gas you do not have to fill up until Te Anau on the way back but this is one of the routs where you are going a long time without seeing a gas station so plan ahead.