I can certainly help you get started. I live in Australia, but am from NZ, so can provide some suggestions for both.
New Zealand
If sleeping in huts is a priority, the major tracks in Fiordland, NZ will be a good choice. Check out the Milford (though is a bit 'touristy'), Routeburn, Hollyford and Kepler Tracks. All will take you through mountainous country, are physically challenging (though you don't need to be an Olympic athlete!) and can be completed in 3-5 days. (If the stars align, I hope to be walking the Kepler with a few friends and family next February.).
Fiordland has frequent rain all year round, with the addition of cold and snow in the winter months. In the warmer months you have to contend with swarms of sand flies! If you are traveling in spring (or autumn), you just might get a little less rain and bugs!
Other areas I can recommend for hiking are Stewart Island (the real south island!) and the Arthur's Pass region. I spent a week walking the 3 Passes Route near Arthur's Pass in Feb 2013 and would definitely recommend it to anyone seeking a more challenging walk away from the busier major tracks. There are shorter and longer walks in the Arthur's Pass area too.
If you have 3 months to spare you might like to try out the Te Araroa Trail, which entails a full traverse of the north and south islands.
www.tramper.co.nz is a great hiking resource in NZ (the Kiwis call it 'tramping'). The Dept of a Conservation has a long list of NZ tramps
Australia
I live in Melbourne, in the state of Victoria, which is in the south eastern corner of the continent. It is an excellent area for hiking. The best hikes (for the fit and adventurous) are in the alpine country and for this the best reference is the book "Bushwalks in the Victorian Alps" by Glenn van der Knijff. You can get it online from Open Spaces Publishing. A good online (free) source of information is the Australian Alps government site.
Other multi-day walks in Victoria I can recommend are the Great Ocean Walk, the Great South West Walk and both the Northern and Southern Circuits at Wilson's Promontory.
Generally, huts are not readily available in Australia and you should plan to carry your own shelter. That said, there are huts in the Mt Bogong circuit walk, which is included in the above book and which I blogged about last September.
You might also want to look into the Australian Alpine Walking Track, which traverses the alpine region that extends from Victoria to NSW. To do the whole track takes around a month, but you can also do sections of 3-7 days. Have a look at John & Lyn Daly's AAWT site as well. Karen Cody's site includes a ton of detail about segment times, altitude gains, etc.
Less traveled (or maintained) is the McMillan Walking Track, a 10 day 220 km trail which passes through some of the more remote parts of the Victorian alpine region. See also this trip report.
In New South Wales (NSW) a popular high country walk is the Mt Jagungal Circuit. See John Chapman's site.
Tasmania has some amazing walks though these are generally very rugged and remote, and mostly suitable for experienced hikers only. Walks of note are the Overland Track (a 5-6 day walk, which also has huts!), Walls of Jerusalem, and, for those seeking a challenging walk with amazing scenery, the Western Arthurs traverse - see also the photo gallery on Geoff Wise's site.
Situated in the Northern Territory in the heart of Central Australia, you will find the Larapinta Trail, a 223 kilometre walking track, running west from Alice Springs. See also the Travel Outback Australia site and this end to end walk report.
A great general resource for Australian hiking is the Bushwalk Australia forum. Make sure you check out the local track sub-forums, which have information specific to each State - particularly for Tasmania, Victoria and NSW.
Finally, PCT and AT junkies might like to check out the Bicentennial National Trail, a 5,330 km trail that spans the east coast of Australia.
Critters
You need to be aware of the key differences in fauna between NZ and Australia. In the NZ bush, you may encounter native birds and lizards as well as the introduced species - rabbits, deer, pigs, ferrets. ie. It's a pretty safe place to be in walking around in shorts. Australia, on the other hand, is home to a wide variety of mostly-friendly marsupials - wombats, koalas, kangaroos, wallabies - as well as an array of nasty creatures, including the most venomous snakes in the world, crocodiles (in the northern regions), a variety of poisonous spiders, centipedes and scorpions. You need to be careful out there and gaiters are a good idea in the hot months. (Ok - maybe there is one creature in NZ that is scary enough to warrant mention - the native weta - man, those things are freaky.)
Maps
In regards to maps, you can get excellent 1:25,000 and 1:50,000 topographic maps for Australia from stores like The Melbourne Map Centre. These topo maps can also be bought online from Mud-maps, to use with their handy iPhone application, which is my route-finding tool of choice.
For NZ maps try the free maps at www.nztopomaps.com or the government service here.
Anyway, that should get you started. Comments and suggestions for additional content for this post are welcome.
[The post does not include any info on walks in Queensland, South Australia or Western Australia - let me know if you have some suggestions and I will add them in.]
Cheers
Andrew
