iPhone airplane mode to avoid roaming charges
Turning your phone to airplane mode will shut off all external communication but as you said you can turn on wifi when necessary. If you manually turn off data roaming, you should not be able to access data networks that are not your home carrier in Australia. thus you should not get any data charges. I did this when traveling in SE Asia and got no charges.
For time zone, you probably have to manually change this, and then change it back when you return to Australia.
My understanding and experience is that the GPS will still work, but won't be very accurate as a lot of that functionality is based on cell tower triangulation. This will be especially true in NYC where the tall buildings will interfere with the GPS signal that gets to the already weak iPhone internal GPS antenna. You could turn off data roaming and leave the phone service active, and this should help as long as the map data is preloaded on the phone.
iMessage will work over wifi.