NYC is actually among the safest as far as murders go. In the 1970s they had roughly 2,300 murders/year. It's now below 600 as you mentioned. That's for 8 million people. Also, the bulk of murders now are gang violence or drug-related. When an innocent person is murdered in NYC it's a big deal.
I would credit Rudi Guliani for that progress, certainly not the NYC gun laws. Criminals (and pro Football players) still have no trouble getting guns.