We drove from Blenheim to Christchurch, and the drive had some beautiful scenic spots along the coast. Christchurch is a charming town. Do not miss Queenstown. We didn't love Dunedin, nor did anyone especially, on our tour. I would definitely to Milford Sound, but, if you driving, keep in mind that the road there has some very windy spots, and the dark tunnel you go through is only one and a half lanes, for two way traffic, including buses! You may need to back up into a little cubby, while in there, to make room for a bus!

Franz Josef Glacier is impressive. and an easy hike for those who desire to go up to it.

I describe New Zealand as my favorite country, and I would plan as much time as possible to thoroughly explore it. You won't be disappointed. My advice would be to do the North Island first, because it has many special spots which are impressive, till you see how impressive the South Island is. The two islands are very different.

We found it very easy to travel around both the North and South Islands of New Zealand on our own in a rental car. When we visited the South Island, friends traveled with us, so we rented a van. We rented a car when we visited the North Island by ourselves. We enjoyed getting around on our own, staying at Bed and Breakfasts, and mapping our own itinerary. New Zealand is one of our favorite countries. We spent around 2 1/2 weeks on the South Island on one trip, and 2 weeks on the North Island on another trip. We had to split it since we were working at the time, and had a limited number of vacation days.

There is so much to see in New Zealand. You might want to visit only the South Island if you want to travel leisurely.

From my notes:

In Christchurch, we loved the Botanic Gardens. I also recommend a boat ride on the Avon, and a visit to Willowbank Wildlife Reserve to see the kiwis. The International Antarctic Center was also extremely interesting.

Kaikoura has a lovely setting - a good place for shoreline walks. You can also take a whale cruise from there.

Blenheim and the Marlborough Wine Trail are very interesting, if you are into wine tasting. Lots of excellent wineries.

Abel Tasman National Park is absolutely beautiful - a great place for short or long hikes.

Punakaiki Pancake Rocks and Blow Holes in Paparoa National Park are an interesting stop.

The helicopter flight over Fox Glacier was a fantastic experience. (Book early for this.) You can also hike to the foot of the glaciers. We loved the Minihaha rainforest trail nearby - what a contrast to the glaciers a short distance away. You will probably see mountain parrots in the parking lots for Fox or Franz Josef glacier.

We were a little disappointed in Queenstown. It has a gorgeous setting, but is extremely touristy. We did watch the bungey jumping at the Kawarau Gorge Suspension Bridge on the main road into town.

We loved Te Anau and it was worthwhile to visit the Te Anau Glow Worm Caves. The city is situated on a beautiful lake. We took the Fiordland’s Doubtful Sound trip from Manapouri, which was fantastic.

And of course the lake cruise at Milford Sound was great. At Milford, you can take a 30 minute walk to the spectacular Bowen Falls.

We enjoyed Dunedin. It's a college town. Don't miss seeing Baldwin Street – Steepest street in the world (better than Lombard Street in San Francisco). From Dunedin, you can sightsee on the Otago Peninsula, where you can see Larnach Castle, the Royal Albatross Colony, and Penguin Place.

Mount Cook National Park is also a very interesting destination. There are many trails from the visitor center there. Also, between Mount Cook and Christchurch, is Lake Takapo - absolutely beautiful.

In Auckland, be sure to see Kelly Tarlton’s Southern Oceans Adventure (Underwater World) – antarctic exhibit with a colony of live king penguins. Auckland is an interesting city to visit - a beautiful setting. While you're there you can go to Muriwai Beach and see the Gannet Colony – 10km from Auckland.

An interesting stop after leaving Auckland is the Waipoua Kauri Forest - one of the world's largest trees.

The Bay of Islands is an interesting stop - be sure to take a cruise there.

We loved the Coromandel Peninsula. It is a rugged and densely forested region that has some of New Zealand’s best beaches and scenery. You can also see the Karaka Bird Hide shelter to look for shorebirds on the extensive mud flats.

Of course you don't want to miss Rotorua. Be sure to see the Te Whakarewarewa Thermal Area, the Orakei Karako Geyserland, the Waimangu Volcanic Valley, and the New Zealand Maori Arts & Crafts Institute. There are lots of other thermal areas to visit here also.

Napier is an art deco town - beautiful to visit. Kiwi House has Kiwis and other birds. You can actually feed and touch kiwis there.

The Hawkes Bay area has many wineries. At Cape Kidnappers, you can see the world’s largest known mainland colony of Australasian gannets.

At Wellington, don't miss the Te Papa Museum of New Zealand. The Maori and Pacific Island collections are outstanding. It is a very long ride to Wellington, though.

En route to Lake Taupo, you can see the Mt Bruce National Wildlife Centre - Kiwis, Tuataras, and Takahes. Just north of Taupo, see the Huka Falls.

Have fun planning your trip. I find planning half the fun.

I've been to Australia ten times and traveled from the top (the Kakadu, Darwin, Litchfield NP, Bathurst Island) to the bottom (Tasmania) and to places in between (Lord Howe Island, Sydney, Melbourne, Brisbane, the Barrier Reef, Cairns, the Daintree, Broome, Exmouth, Perth, Albany, Margaret River, Adelaide, McLaren Vale and Barossa, Kangaroo Island, Canberra). I've also visited New Zealand four times, though I have not visited its very northern end (just made it as far north as the Bay of Islands), nor its very southern end (Milford Sound was the best we could do, and we had to cancel a trip to Dunedin and more southerly parts due to very stormy weather once).
I love both countries. However, I would have to say that if you are interested in birds and other wildlife (these along with wine and art are my interests, as well), Australia offers the greater variety. Its Kakadu is especially rich in wildlife and, as this is the dry season for the Top End (May to October), the wildlife concentrates around and in bodies of water. I have never seen so many colorful and unusual birds in my life. You would have to fly into Darwin from Sydney (a long and usually expensive flight, but at least Virgin Blue offers discount flights if you can purchase well in advance). From Darwin, you can take a several day tour into the Kakadu, which is not only rich in wildlife, but in aboriginal culture--you can visit ancient rock paintings here. The landscape is breathtaking--my husband, who is originally from Florida, says it looks like a cross between the Everglades and the American Southwest, a mixture of red rock country and wetlands. From Darwin, you can also take a tour to Litchfield National Park, where you can swim in crocodile-free rock pools while the black cockatoos and flying foxes fly overhead.

Posted my message too soon. I wanted to add a few things. The Kakadu contains more than 60 species of mammals, 289 species of birds (more than a quarter of all Australian bird species), 132 species of reptiles, 25 species of frogs, 55 species of freshwater fish and over 10,000 species of insects.
For seeing marsupials, Kangaroo Island near Adelaide was my favorite. They're everywhere! The island's waters also have an abundance of wildlife: dolphins, seals, sea lions, leafy sea dragons, and, at certain times of the year, whales.
You will see beautiful, unusual birds throughout Australia, even in Sydney you will see cockatoos in the Botanical Garden and ibises foraging like pigeons right at The Rocks. Each area of Australia seems to have something special. Northern Queensland has cassowaries. On the Eastern seaboard (east of the Great Dividing range) and also in Tasmania, you'll find the spectacular lyrebirds. Lord Howe Island is home to masked boobies, fleshy-footed shearwaters, red-tailed tropicbirds, sooty terns, and endemic wood hens (very rare, I never found one, though tried). Kookaburras and black swans are found in many regions of Australia (and sometimes in NZ).
New Zealand also has some wonderful birds that you won't find in Australia, but I would say the variety and numbers are greater in Australia. However, if you are going to NZ and if birds are a main interest, I think Stewart Island probably would be worth your time. (I've not been there, but have wanted to go.) I would emphasize the South Island over the North Island because of its stunning natural landscapes and wildlife.
Can you perhaps manage more than 21 days? After all, if you are traveling from the U.S., you will have to endure some long flights and the expense associated with these flights. You should make the most of your vacation.