You should check this out:
http://www.nyc.gov/html/nypd/html/pct/cspdf.html
Its the page that lists all the crime stats by borough and precinct. If you look at the 10-year stats just about every major category shows a large double-digit drop, making NYC the safest large city in the country. I can tell you that crime in every precinct is also mapped out with coded pins on each location so that the command can allocate its resources accordingly. Each precinct commander is then held accountable at monthly Compstat meetings and raked over the coals if criminal patterns are not addressed.
I think there is lots of room for improvement though, and with the budget cuts the department is already doing more with less while crime continues to fall. But this isn't an exact science. Criminals have a lot of places to hide along with people willing to shelter them. A lot of crimes produce either no willing witnesses (especially with regard to drug or gang-related acts) or useless descriptions of the perp and then you're left with nothing to go on.
The three easiest things that would improve matters actuaqlly have little to do with us. I'd like to see fewer petty criminals released with "time served" or put on parole/probation. There should also be a LOT more people in institutions for mental health. They don't seem to rob or steal that much but they do often snap and violently assault people (including us). I'd also like to see concealed carry on a "shall-issue" basis for New Yorkers but I'm not holding my breath.