Looking for an interesting place in Australia or New Zealand to spend a month or so from mid-Sept to mid-Oct. (Could possibly be split between two destinations for two weeks each.) Would like it to be warm, ideally coastal or desert, not a big city but not a tiny town either. Great if there are some sights and daytrips nearby, though I'm not very sporty or outdoorsy. Have a writing project so will be fairly busy, but other than good Wifi, don't need much. Something quirky and offbeat would be ideal. Any suggestions? Thanks!

Coming from the UK? It's a long way to travel for a one-month stay and your first week is likely to be disoriented by jetlag.
In Australia you could look at Byron Bay and surrounds, or Nimbin if you want serious quirkiness (to the point of distraction, maybe).
Or Canberra. Not as warm in September as the places mentioned above but quirky in anyone's terms yet also well-serviced.

Why Australia/NZ?
It's a long way to go just to find some warmth in which to write in and a month isn't much time when you're travelling half way round the world.
While I share some of the reservations about Australia-NZ for just a month, I will nominate Noosa on the Sunshine Coast, and Russell in the Bay of Islands NZ ... both excellent for writing, and a car isn't required. But why not look at a place in - say - the Caribbean?

Hmm, I'm kind of surprised by these responses so far. A month feels like a long time to me, and Australia and NZ aren't that far. (I've flown to Australia before for 10 days...) I'll certainly look into the places you suggest. Thanks!
In one way you're right ... a month is a fairly long time - basically anywhere in the world.
Perhaps we are (a) recoiling, because we have to do the 14-22 hour flight every time we travel, and (b) applying our normal time-frame for people who wish to explore Australia, rather than rent an apartment and hit a keyboard.
Anyway ... Australia (Queensland) will be substantially warmer than anywhere in NZ if temperature is a key factor.

Ah, yes, I see what you mean -- the travel distances are great within the countries, as well as to get to them. I'll actually be en route for a several-month stay in Bangkok, so the trip is not quite as out-of-the-way as it may have sounded.
Any thoughts on Cairns, Darwin or Brisbane?
Any thoughts on Cairns, Darwin or Brisbane?
I have lived in all three. Without a car, I would rank them Cairns, then Darwin, then Brisbane.
Cairns will be humid and nice (about 28°), Darwin more extreme (about 33°), while Brisbane weather would be close to perfect. All three are more similar to Bangkok than different. Brisbane is a big city, and fairly expensive in the desirable areas.