Flights from New York to Australia?

I need help finding flights to Australia this winter. We can either leave December 22 or December 23. I have already looked, and I can't find anything logical (meaning without a million stops). We can really leave anytime, but we have to be back by January 3. There are four of us going (there are 5 in my family but my oldest daughter is going to be in Hong Kong). How do I get there without a million connections or any crazy prices? We can fly in and out of any airport in Australia. Also flights back would be appreciated and an itinerary of where to go. If you include the itinerary, there must be some time in Melbourne because I used to live there. Thank you!