Hi,
One of my friends and myself are looking to move to america this August or September from australia and are trying to find cheap apartments in New York, brooklyn, calafornia, miami or somewhere in this area or anywhere close to these places that are cheap. To me cheap is about $150 to $200 Australian dollars each a week.
Can anyone please give me any ideas of places to look, areas to look or is anyone wanting to rent a property at this time or know anybody wanting to do so?

Many big city newspapers have their classifieds online, so that would be my suggestion on where to browse for prices.

Also, you can check with the larger apartment sites and search by city, apartment size desired, maximum price, etc:

Search thousands of apartment communities nationwide! - ForRent.com
ApartmentGuide.com - apartments for rent, apartment finder

PS. I forgot about a relative newcomer - but an awesome resource too:
craigslist: san francisco bay area classifieds for jobs, apartments, personals, for sale, services, community, and events