Visit the Milford Sound
If you have a day to spare in Queenstown, you should take a day excursion to Milford Sound, one of New Zealand's most breathtaking sites that will make you feel little and humble as you travel through these enormous mountains. The Milford Sound, a fjord, not a sound as the name suggests, is considered to be one of the most visited places in the world. It is located in the stunning Fiordland National Park and sees over 250 days of rain but even in the rain, the place still looks incredible.
There are many operators running day trips to the Milford Sound from Queenstown that includes a shuttle bus from Queenstown to Te Anau and back, a cruise along the Milford Sound, and several photo stops along the way to the Milford Sound which is one of the most scenic roads in the country. A trip to the Milford Sound from Queenstown costs about 126 USD per person including lunch and it will take about 9 hours so you can expect to spend the entire day there.