Best Amazon AWS region for Australian website?

I would suggest that the answer is now Sydney, Australia!

http://aws.amazon.com/about-aws/whats-new/2012/11/12/announcing-the-aws-asia-pacific-sydney-region/

Ping times from a residential ADSL2 connection in Melbourne:

$ping -c 10 ec2-54-252-25-79.ap-southeast-2.compute.amazonaws.com
PING ec2-54-252-25-79.ap-southeast-2.compute.amazonaws.com (54.252.25.79): 56 data bytes
64 bytes from 54.252.25.79: icmp_seq=0 ttl=49 time=29.044 ms
64 bytes from 54.252.25.79: icmp_seq=1 ttl=49 time=30.983 ms
64 bytes from 54.252.25.79: icmp_seq=2 ttl=49 time=29.424 ms
64 bytes from 54.252.25.79: icmp_seq=3 ttl=49 time=30.563 ms
64 bytes from 54.252.25.79: icmp_seq=4 ttl=49 time=31.842 ms
64 bytes from 54.252.25.79: icmp_seq=5 ttl=49 time=31.564 ms
64 bytes from 54.252.25.79: icmp_seq=6 ttl=49 time=30.730 ms
64 bytes from 54.252.25.79: icmp_seq=7 ttl=49 time=30.797 ms
64 bytes from 54.252.25.79: icmp_seq=8 ttl=49 time=32.737 ms
64 bytes from 54.252.25.79: icmp_seq=9 ttl=49 time=30.984 ms

--- ec2-54-252-25-79.ap-southeast-2.compute.amazonaws.com ping statistics ---
10 packets transmitted, 10 packets received, 0.0% packet loss
round-trip min/avg/max/stddev = 29.044/30.867/32.737/1.024 ms

Sweeet!

NOTE: I don't know why this got downvoted. To me the general question is how to choose a good location that is near (for certain definitions of near) your main audience.

In my opinion the distance that is mainly important is hop-count. If you find a route from your location to your server that has 3 hops vs a location that has 20 hops the choice should be clear.

Of course routing stuff may change and just choosing by using only your provider isn't quite enough. I'd get accounts from the majority of large ISPs and do some tests.

What test? ping times and hop counts. By ping tests I don't mean do a one time test with 4 pings. Let it run a week or so and do the math. (min/max/avg, standard deviation, packet loss etc. -- yes ping will tell you, just be sure to save the data somewhere in case you find a question that ping won't tell you out of the box) That should give you at least a basic idea of how wether you'll have to expect slowness because of the location.

Hop count is the same. Let it run for some time and do the math again.

With that being said: If you don't know wether it'll matter that much you probably shouldn't care about it. If you know that it'll matter how good the link is between your main audience and yourself I have a feeling that EC2 may not be the best choice in the first place. I don't think you'll get any support if you find that the performance is lacking. I'd rather talk to a service provider that is more open to customer requests and that will respond timely for exactly these kinds of problems.

On another note: Do you really know that your audience is in a certain location or is this just an "australian site" because the people who make it are from australia?

I agree with the gist of this question. I am located in Australia and I was using AWS with a Web Console for a server located on the East Coast region.
As the Console used AJAX extensively, network latency made the console unusable.