Warning: Long post!
I spent 3.5 weeks driving around the South Island and 1 week on the North Island in February of this year. Definitely rent a car. The South Island is fairly easy to drive. The towns/cities are very small and simple to navigate once you get used to the constant reverse round-abouts. The rural roads are decent, but mostly single lane and there are a lot of tight mountain passes and single lane bridges throughout the country.
We ended up booking our accommodations as we went based on weather and developing interests. This meant sometimes staying in hostels, airbb, camping, and one night sleeping in the car. I personally wouldn't do it any other way as it gave us the flexibility and freedom to change the trip and not be stuck in a place we had no interest in. Camper vans are also extremely popular in NZ and rent-able for reasonable prices. That's something I would also consider next time I visit.
We flew into Christchurch, spent the night to recover from the long flight and drove to Arthurs Pass. Amazing alpine environment, but from my research the weather is very hit and miss. We lucked out and had 3 days of clear skies. We hiked the Avalanche Peak/Scotts Track loop which was my favorite day hike in the area. We also did Bealey Valley (which was a beautiful hike up a valley to a seasonal hanging glacier), Temple Basin (great views), and a few of the short waterfall hikes (Devils Punchbowl etc). On the way out of the area we hit up Castle Rock which was OK for stretching out the legs, but not much more.
We then drove through Lake Tekapo (check out the white bluffs if you're camping in the area) and then to Wanaka/Queenstown. Wanaka is quiet and quaint whereas Queenstown is touristy, busy, and bustling with lots of attractions. A lot of good hikes in the area, but we had a few days of bad weather so we only did Diamond Lake/Rocky Mountain Loop, Mount Crichton Loop, and The Iron Mountain in Wanaka.
From there we drove through Hast Pass in a torrential downpour which sucked for driving, but created some out of this world waterfalls. Some crashing down right onto the road. From there we hit up Fox and Franz Glacier which I found kind of disappointing. The glaciers in the Rockies are far more impressive, although being next to a glacier surrounded by rain forest is a new experience. The glaciers have been shrinking at an extremely rapid rate and are far less prominent than they once were. We did the two valley hikes and did the Roberts Point Track at Franz Josef Glacier which was the highlight of the area for me. When I go back I will probably skip the West Coast, Glaciers, and the infamous sand flies.
From the Glaciers we drove up the coast, hit up some small drive up spots and headed towards Nelson. We took a stop and hiked the Mount Robert Loop off HW63. Great mountain hike, but it was a bit tougher than we were expecting from the descriptions we read. Maybe we were just tired from driving.
The rest of our stay was based out of Nelson. We did a bike wine tour in Blenheim to give our legs a break (which was a lot of fun), did the North portion of the Abel Tasman great walk as a day hike (basically tropical beach walking), hit up Wharariki Beach at low tide (definetly recommend it although its out of the way), and hiked Cape Farewell/Pillar Pt Lighthouse which gives great views of the ocean and rugged coastline.
From Nelson we flew (cheaper and faster than the ferry) to Wellington to continue our adventure on the North Island. I honestly enjoyed the South Island way more than the North. It's more rugged, has a lower population density, more trails, and a friendly relaxed atmosphere. Everyone we met was extremely helpful and friendly.
There is still a lot of the South Island we didn't see, but thats for another trip. We meant to hit up Milford Sound, but it was pouring for the next few days when we had the chance so we opted to skip it. Mount Cook/Hooker Valley is another area I really wanted to check out but we just didn't have time. I'm only half way done processing my photos from the trip, but I've attached a few of the places I mentioned to give you a feel for them.
Hopefully that was helpful. If you have any questions about the trails I listed, country, driving, whatever shoot me a message or post here.
My wife nearing the Avalanche Peak Summit (gives an idea of the terrain)
Kea bird at the summit
Incredible 360 views from the summit
Bealey Valley Scrambling
White Bluffs of Lake Tekapo
Rocky Mountain/Diamond Lake
Franz Josef Glacier
Roberts Point at Franz Josef - neat steel walkway built right into the cliff face.
View from the end of Roberts Point