Be VERY,VERY careful.NYC real estate laws are so different to Australia and legal short term apartment rentals are few and far between.My son owns an apartment in Manhattan and basically is not allowed to rent it out.
A lot of newer apartments are condominiums and so a bit more flexible.However my sons in laws own a condominium in NYC that we stay at at times.To do so we have to be approved by the board and submit photos before staying.
Go for the apartment hotels such as Affinia or Radio city apartments.Oakwood apartments could be tried but usually for a month or more.
Dont be fooled by someone saying that they have stayed at apartment X or Y.That doesnt mean it is legal and if you are the bunny who is caught you can end up on the street sans money.A lot of apartment rentals in NYC are also out and out scams.