Apartment Hunting

I've been looking for a place for a while, since my current neighborhood is not wonderful and in fact features nightly screaming matches between a rotating cast of men and women outside my window (free entertainment?). However, as everyone knows it is freaking expensive to find a place in NYC. Forget Manhattan, even the boroughs are expensive. I have heard that if I get a couple Chinese language newspapers they might have some cheaper apartment options in them. This would be a better tip if I spoke Chinese, but hey, I can work around that. So hopefully I will soon find a little place for myself and the kitties somewhere safe and cheap. I am accepting advice from anyone who has apartment hunting tips for someone on a kind of ridiculous budget.