New Zealand/ Australia tours

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Be very careful when looking at tours to Australia and New Zealand. It used to be that you only had to pay for the airfare to get you to Australia and New Zealand and all of the internal flights were paid for as part of your tour. They have changed their policy and now most companies either make you make the internal airline reservations or they will do it but the cost of those flights are NOT included in the price of the tour. If for some reason, you cancelled the tour within the allocated time frame, you are still liable for paying all of the airfares. We returned in March from a 20 day NZ/ Australia tour by Holiday Vacations and just loved it. Everything was included except Tour Director tips and bus driver tips, but there were no options like other tour companies try to sell you on. All airfare was included. Our tour director even boarded the plane in LAX and flew back to LAX with us. Take a look at their on line brochure and see if they are going to where you want to go. They offer a number of tours there.

If you like to hike and do not wish to spend much time in cities, I would suggest one of these for an active tour exploring the scenic wonders of the South Island of New Zealand by hiking, kayaking, and glacier trekking.

https://www.rei.com/adventures/trips/pacific/new-zealand-hiking-kayaking-south-island.html

http://www.mtsobek.com/trips/the-pacific/new-zealand/wild-west-coast

We have used both companies for hiking trips in Patagonia and Slovenia, and can recommend both for quality of the guides, food, lodging, and activities. You could add Australia on your own, flying to Sydney or Melbourne. These are cities, but Sydney in particular has a lot of nice walking and outdoor activities to offer.

But I would encourage you to also consider independent travel. We did that for The South Island of New Zealand (plus Sydney and Melbourne), and it was a great trip. We did a mix of grain, self-drive for a week, and a multi-day guided hike on the Milford Track, staying in nice lodges with all meals included.

if you need to fly within australia, for domestic companies look at Qantas, Jetstar ( a cheaper version of Qantas) and Virgin Australia. ( if you do happen to book any of these, check that baggage is included. Also the carry on will have a weight restriction ( ''typically'' 7kg)
Australia , as you probably know is large ( think Northern USA) so cheaper domestic flights might be worth considering.
Sydney has some wonderful walks ( it is surrounded by national parks) for example, within an hour or so on the train you can be in the Blue Mountains ( some sydney residents commute from there)
https://www.visitnsw.com/destinations/blue-mountains?nst=0

Australia has many national parks, that are so varied, be it coastal or inland. each state has its own national parks eg:
https://www.nationalparks.nsw.gov.au/visit-a-park/parks/kosciuszko-national-park

http://www.visitvictoria.com/Things-to-do/Nature-and-wildlife/National-parks-and-reserves
really depends on what you like to see/do.

Both Australia and NZ are very easy to tour around, the cities are not huge and there are plenty of tourism resources to help your planning.
https://www.australia.com/en

think long and hard about what/where you visit, depending upon the time of year. eg: can be hot in the summer etc

hope this helps.

New Zealand is still on my bucket list so I can't give first-hand advice on specific tours. However, I have had good experiences with a couple of tour companies elsewhere. It is pricey but I'm sure Natural Habitat Adventures' "New Zealand Nature Explorer" is spectacular. I'm sure Intrepid also operates good tours since they are Australian.

If you really have your heart set on exploring the two countries via tours, you might consider basing yourselves somewhere and just doing day trips rather than spending money for some sort of all inclusive, guided experience. As others have opined, exploring both Australia and New Zealand as independent travelers is pretty easy - air travel within each is cheap and efficient. Driving is straightforward too once you're outside of the large metro areas.
New Zealand in particular is better explored independently via car IMHO. The only metropolitan areas that really qualify as cities are Auckland, Wellington and Christchurch. Our favorite place for hiking is the area in the vicinity of Queenstown - the trail heads for several of NZ's Great Walks are nearby and are easily accessed by car. That said, the opportunities for hikes, scenic walks, and just enjoying the spectacular scenery in general (on both North and South islands) are too numerous to catalogue. Better to grab a few guide books, do a bit of research, then craft an itinerary that covers your own particular interests.
As was mentioned the Sydney metro area (including the Hunter Valley, the Blue Mountains, and the beaches) has enough to keep you busy for a month, and the city itself (in our opinion) is the most beautiful on earth.
I apologize if this isn't what you want to hear but organizing your trip independently, with the occasional day trip thrown in for good measure, will allow you much more flexibility than what you're proposing, will be a lot more fun for both of you, and will be much cheaper in the bargain.

We had a wonderful trip to Australia/New Zealand with Odysseys-Unlimited in March of 2014. www.odysseys-unlimited.com

We did a great tour of the North Island of Australia with AAT Kings (affiliated with Trafalgar).

For Australia, you don't need to take an escorted tour, but I recommend visiting Perth, Darwin, Cairns, Sydney and Melbourne. Don't miss the Blue Mountains and Hunter Valley near Sydney or the Great Barrier Reef from Cairns. The Great Ocean Road and Phillip Island Penguin parade are south of Melbourne and a MUST DO.