My husband and I went to Australia and New Zealand's South Island for most of January, 2015. We spent 2+ weeks in New Zealand, and 3 days in Australia on either side of New Zealand. We are avid hikers and generally include a lot of hiking in our trips, and New Zealand was no exception. The best thing we did, and what I would recommend to you, is the 5-day guided Milford Track trek with Ultimate Hikes.
The Milford Track has justly earned its reputation as one of the world's great treks. And the only way you can do it is self-guided, staying in the rustic huts along the track, or guided with Ultimate, staying in very comfortable hotels they have built along the track. No other company can use those hotels, so Backroads and other travel companies cannot lead tours on this track.
Everything about the trip was topnotch---the transport to and from the hike by coach and boat, the guides (very professional but lots of fun), the accommodations (we booked a private double room with ensuite bath for each of the 4 hotels), the food ( excellent in every way, with nice 4-course dinners with a choice of main), the scenery, the camaraderie of the other guests (our group was almost 50-50 Australian and Japanese, and we were the only Americans). We enjoyed the evening pre-dinner gatherings in the bar, socializing with the other guests and sipping a glass of wine.
The trip is 5 days/4 nights, starting and ending in Queenstown. They take care of everything, from the pre-trip meeting the night before departure to the cruise on famous Milford Sound and coach ride back to Queenstown on Day 5. There are 3 full days of hiking, around 10 miles each day, but it is mostly fairly level and easy walking. The one big ascent has a climb of 2400 feet over a pass. The scenery is peaks, cliffs, waterfalls, rain forest, rivers . . . All by way of a well-built and safe trail.
Cost for the trip in January 2021 is $2730 NZD, which comes to about $1965 in US dollars. It will be more in January 2022, but not a great deal more. Compare that to the $5400 or so that Backroads wants for their 9-day/8 night South Island hiking trip. That trip is longer than you want, and the itinerary did not look all that great to me---most days the hike is only 3 or 4 miles. They do include a cruise on Milford Sound, but none of the walking on the track itself.
We have done a lot of hiking around the world---Swiss Alps, Italian Dolomites, Patagonia, and Japan are all wonderful, but the Milford Track stands out in our minds as a unique adventure.
You could add to that with some of what we did on our 2015 trip that did not involve renting a car. (We did rent a car for one week, to tour from Christchurch to Queenstown, but I will leave out that part).
Starting in Christchurch, we took the train north up the coast to Picton. There we met a water taxi that took us out to an eco-Lodge on the Queen Charlotte Track ( hiking and kayaking on offer).
After two nights there, we returned to Picton by water taxi and caught a coach to Nelson, a city famous for good food and wine. We used this as a base to explore Abel Tasman National Park, but one could also book a 2-or 3-night stay in the park at the lodges, with hiking and kayaking. (I will have to find the name of the company that offers this as a tour from Nelson).
Then fly from Nelson to Queenstown for the Milford Track. Add several days in Queenstown to explore the town and the adventures offered all around there---rafting, bungee jumping (fun to watch, even if you don't care to jump).
That should more than fill two weeks. How much time will you have?