As a fellow Australian who currently lives in NY I hear where you're coming from. For obvious reasons this is very attractive to Australians.
First up, as already mentioned here, you need to know your exit strategy. Is this short term or long term hold? Are you looking for cash flow? Probably not. Seems like you are thinking capital gains in the long term to me. I suggest you find a good lawyer who understands the tax implications both here in the US and for you as an Australian. Do you currently reside in Australia or elsewhere? I have a NY based law firm who specialises in just this kind of transaction as I have been working with others like yourself looking to make hay while the sun is shining.
If I had $600k in cash, I'd use it as a deposit on the three apartments you are hoping to acquire. There are banks that will provide up to 65% LTV and I'm more than happy to make the introductions for you. As you do not indicate whether this is your limit, I'll leave it at that. If this is your limit, however, and you still wish to follow this route, I would suggest looking in either upper Manhattan, such as Harlem, or in Brooklyn neighbourhoods such as East Williamsburg or even Bushwick.
While these areas may not be in trophy areas, they are in your budget. With $600k you can really only afford one, maybe two properties, however this will be a stretch. I would suggest one and keeping reserve funds for common charges, taxes and unforeseen expenses. Returns are around 6% give or take. Doesn't sound so great unless you understand the potential upside - and again, I'm sure you do.
As a final note, the foreclosure crisis has not affected New York City as much as it has others such as Detroit, Phoenix, and much of Florida. You will be hard pressed to find such 'deals' here as many savvy buyers recognise the inherent strength of the market. It is a global capital of media, technology. art, fashion, finance and learning. Many corporations are based here and consequently, demand has only slowed, not ground to a halt.
All the best with your hunt.