Another alternative to thousands of cops and hundreds of cameras would be for the people of NYC to persuade their keepers to let them have defensive weapons, or better yet, just acquire them anyway in open defiance of self-defense tool bans.
The number one defense against crime, though, is to put the hoodlums in jail and let them rot, or better yet, execute them. If you put a criminal in jail for life, you end a lifetime of crime. But you can't do that unless you can catch them. And that is what the cameras are for. Guns are OK if you can carry them and you have the opportunity and ability to use them, but you shouldn't have to meet all those conditions in order to be safe from crime.