Can anyone give me links for online local/national "newspapers" for each of these countries?
I'm thinking it'll be interesting to check on now and then and right before I leave (find out what latest things the locals are talking about).

Sydney Morning Herald

http://www.smh.com.au/

The Age (Melbourne)

http://www.theage.com.au/

New Zealand Herald

http://www.nzherald.co.nz/

If you want to get even more local, here is a website with links to newspapers, radio stations and TV stations in small and big towns throughout Australia:

http://www.kidon.com/media-link/australia.shtml

Same thing for New Zealand:

http://www.kidon.com/media-link/newzealand.shtml

Same thing for rest of Oceania:

http://www.kidon.com/media-link/oceania.shtml

Oh yes, another one that probably deserves to be mentioned is

The Australian

http://www.theaustralian.news.com.au/

Perfect! Thank you!

i like to use..

www.newzealandnews.net

www.australianews.net

which offers a summary from, and links to all the national papers

You can also listen in to the ABC (Australian Broadcasting Corporation) at www.abc.net.au.

The Australian is a Murdoch paper, but while it displays a distinct list to the Right an attempt is made to run it as a "quality broadsheet". Heaven knows you couldn't apply that term to any of his other Australian papers.

The Sydney Morning Herald and Melbourne Age are both owned by Fairfax Press and share much material.

If your spending time in Queensland, you could try www.couriermail.com.au