New countries for us (NZ and AUS) and general questions

If you are asking about apartments because you want to cook your meals, note that what is called a “motel” in New Zealand often has rooms with kitchen facilities for self-catering.

In Queenstown we stayed right in town at the Coronation Lodge, in a large bright corner room with a small kitchen area. They also have a one-bedroom apartment.

https://www.coronationlodge.co.nz/

Don’t faint when you see the prices. The New Zealand dollar is only 64 US cents. So take 1/3 off the price you see in NZD.

We are traveling with a sister so with the requirement of two bedrooms and two bathrooms we think we’ll be doing a combination of hotels and apartment rental, especially for our 5-7 day Sydney time. For our first trip to this area we hope to see a few places in the north island of NZ on our way down to the South Island. We’ll spend the bulk of our NZ time on the South Island.

For AU we have a week+ arranged in Melbourne at the end so this time we’ll just go to Sydney prior to Melbourne. We’re appreciative of the vastness and diversity of Australia in particular and know this time we’ll just be getting a glimpse of a small region. We plan to take day trips from our Sydney (yet to be booked) and Melbourne bases.

Thanks so much for your tips about lodging, tickets, car rentals and ferries and sites so far!

We've had good luck booking accommodations thru these guys https://www.stayz.com.au/. Believe they're now affiliated with HomeAway. There are some very nice properties on offer there.
I don't think you quite have enough time to take the Interislander ferry, especially if your destination on the South Island is Queenstown - you'd eat up most of your discretionary time just getting there. Better to fly direct to Queenstown from Auckland, Wellington, or any of the other departure points on the North Island.
Jetstar offers non-stop service from Queenstown to Melbourne and Sydney at reasonable prices. It's the low cost version of Qantas - pretty spartan, and with the usual ala carte pricing for virtually everything, but it will get you where you want to go.
I wouldn't delay locking down your accommodations. NZ has become a popular destination for Asian tourists who visit during the Chinese New Year celebration, which starts in January and can run well into March. During our most recent visit we noted the dramatic increase in the crowds in some of the popular areas ... Queenstown being one of them.

While I think of it: another search engine for accommodations that we've had good luck with is booking.com. Their filters are usually quite helpful in narrowing down the choices on offer, whether it be by location, price, amenities, etc.
As was mentioned Queenstown (and Wanaka, Christchurch, Aoraki/Mt Cook, etc) can get pretty crowded during the height of the season. You'll find that prices for lodging will go down dramatically if you explore just a little bit away from the tourist centers. Staying somewhere just west of Queenstown for example would be handy for explorations along Lake Wakatipu to Glenorchy and beyond. The trailheads for several of NZ's Great Walks are located in the vicinity. In general, we found the Queenstown area was a pretty good base for exploring the surrounding area. As always, getting an early start to your day would help mitigate the effect of the crowds, tour buses, etc.
Another suggestion for a good base would be Te Anau - very handy for a self-drive day trip (or organized tour) to Milford Sound. If you're a bit more adventurous you could join a tour to Doubtful Sound. The departure point for those trips is just south of town in the village of Manapouri. The area was a popular LOTR film location and there are a number of easy hikes that will take you to some familiar locations from the films.
I, too, would probably give Christchurch a miss - it was still recovering from the earthquakes of 2011 when we visited last year - lots of construction going on and the steeple of the Cathedral is still sitting in the middle of the street where it fell 8 years ago. The nearby Banks peninsula is worth a visit however, particularly the delightful French-themed town of Akaroa.
For a first visit to Australia I think your choice of basing yourselves in Sydney and Melbourne and doing day trips from there is a good one - you really don't want the hassle of trying to drive in the big cities, and day trips and tours will be a stress free way to see the Blue Mtns., Hunter Valley, etc.

Tom thanks for the (depressing) link 😢

Knowsley what would you recommend for getting from Sydney to Melbourne by car and stopping somewhere for a couple of nights? We are interest in natural beauty, wildlife and birds when not visiting cities.

It's a 9 hour drive from Sydney to Melbourne. Unless you'd like to devote several days for stops along the way I think that as a first time visitor you'd be better off flying, saving a day, and basing yourselves in the city for day tours from there. As I mentioned before you really don't want to have a car in either Sydney or Melbourne - just more of a hassle than it's worth.
The coastal route to Melbourne is quite pretty but very slow going. If you did opt for a car that way would be my suggestion. Canberra might be a consideration if you want to go the more direct route. The city is basically a gigantic park, and if you did stop for a night in the Aussie capitol you'd be relatively assured of seeing some wildlife ... especially in the evening.

Sydney is (in our opinion) the most beautiful city on earth, with enough to see there and in the surrounding area to keep you busy for a month. One of life's great pleasures is hanging around Circular Quay on a sunny day.

Thanks for the detailed driving information so far. We still haven’t figured out if we’d rather have 2 bases with excursions (no car) and fly between the two cities or rent a car after Sydney to drive to Melbourne stopping for a couple nights along they way. We need to figure out what we’d be able to explore from Sydney (Blue Mountains a must) and Melbourne where we are staying in a home in the Malvern neighborhood.

We still have some flexibility about when and where we end up in NZ and do know that we will fly from a NZ airport to Sydney so we need to pin that down soon. Unfortunately/fortunately we are planning for a trip to Germany that’s rapidly approaching. Lots to consider. Thanks for your invaluable feedback so far!

If you're considering renting a car for at least part of your journey from Sydney to Melbourne, one possibility would be to fly first to Adelaide - one of Australia's most beautiful cities (and best kept secrets). Lots to see in the immediate area - including the Barossa Valley and the seaside suburb of Glenelg. From there you could meander back towards Melbourne along the Great Ocean Road - one of Australia's great scenic drives. There are a number of attractive little towns along the way, and you'll also pass by the Tower Hill Wildlife Reserve near the village of Port Fairy. It's my wife's favorite place - lots of Emus (with chicks) wandering around, grey kangaroos and koalas in the trees right next to the parking lot. Continuing east you could explore Ballarat and the Gold Country NW of Melbourne, and/or divert south to the Mornington Peninsula and Philip Island for the penguins. That would give you a chance to see some of the Aussie countryside before finishing in Melbourne - would think that only 2 or 3 days there would probably be enough to satify your interest.
You really don't want to go anywhere near the Central Business District in a rental car. The local rules of the road regarding the trams is confusing even for experienced Aussies. Find a place to return the vehicle on the outskirts of the city and then make your way to your accommodation from there.

This has all been so helpful! We realize we’ve got to make some hard choices and once we’ve mapped out everything we’ll come back with specific questions. You’ve all given us so much to think about and in fantastic detail. We also appreciate the urgency you’ve conveyed about booking cars, ferries and lodging in high season.

We hope after this introduction to NZ and AU we’ll return for some more in-depth exploring.

Just a reminder that you will be travelling at the end of the school holidays in NZ and things can be booked out or busy (for us). Flights across the Tasman can be more expensive just before schools go back and holiday destinations booked up.