I agree with Jellybean but if you must, then Queensbridge Projects is one of the worst but not as bad as many years ago. Parts of Jamaica, Queens also. Or Lefrak City
Why don t you write about what you know? I m not saying that to be mean, but it would be easier for you to write about things you re familiar with.
Kew Gardens, North Conduit and many others. Check here: http://www.neighborhoodscout.com/ny/quee��
Queens is a great place. Try the Bronx instead. Tailor made for your story.