Australia: Another vote for a week liveaboard with Mike Ball to the outer GBR; was an awesome trip. Cairns is also a great place as a base to do some nature (rainforest etc) sight-seeing.
Further south the HMS Brisbane on the Sunshine Coast is a great dive if you like wrecks. While near Brisbane, Australia Zoo is a good outing; not quite nature, but a great way to see most of Australia's wildlife up close.
If you want to experience the Outback, do a trip out to Uluru (Ayers Rock), spend a night sleeping under the stars in a "swag" and go for an early-morning sunrise hike around Uluru. Be aware you'll need to fly there - Australia is big.
I haven't been out West, but my sister says the diving around Perth is pretty awesome too.
In general, most places in Australia have something outdoors/nature to offer; without a more concrete itinerary it's difficult to suggest specifics.
EDIT: PS: Box-jellyfish are generally not a problem when diving; especially on the Outer Reef. Yes, we have more than our fair share of things which can kill you Down Under, but the dangers are way overblown. Be aware of what might be around, don't poke things, and you'll be fine.
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NZ: haven't dived there, but there's Hobbiton (not exactly nature, but still pretty nifty).
The Tongariro Crossing provides some spectacular views of active volcanoes (we could only go half-way due to eruptions) and is just a daytrip. You'll need to plan either a return hike or someone to pick you up at the other end if doing a one-way hike.
My mum's done the Milford Track and loved it, but that's a bit more of an investment (time and fitness).
Generally NZ has TONS of volcanic areas to visit. Some have facilities such as bathing in volcanic water or even mud.
The Coromandel Peninsula has spectacular scenery and home to the "hot water beach".
NZ is small enough that you can get everywhere driving, although be aware that most roads are single-lane and curvy and will generally take much longer to cover a distance than in other countries.
Haven't been to the South Island so can't personally recommend anything there.