What area of the city are you staying in?
The Australian is on 38th St between 5th and 6th Ave shows every origin live. They open about 5:30am I believe on origin day:
http://wp.theaustraliannyc.com/
I expect origin will get pretty packed so you might want to drop them an email and see about booking a table to be sure you get in.
I haven't watched an origin there myself but did watch Roosters games there for a few weeks running when we first moved over until we got our apartment and cable sorted.
There are also a few aussie cafes downtown that I think open up for origin also, but the Australian has a pretty awesome set up for watching sport (big projected screen plus dozens of plasmas everywhere to watch on).