There are a couple of locks made by lock companies like Abus and Kryptonite that guarantee their locks against theft in New Your city (or anywhere). With these it is more likely a thief cuts the thing the lock is locked to like a bumper or pole than the lock itself.
These lock would have to be cut with a grinder as the metal is big and very hard, even a sawzall would take time.
With a nice bike you will have to lock the frame and the wheels and if you have a nice seatpost then you might just have to take it out.
Otherwise, put the bike inside where it is not seen, and keep it hidden all the time so people don't know what you have. Cover it with a blanket if you have to put it out while you are in for the day. They will be as bold to try to steal it while you sleep.
The only reason the cheap walmark or old Schwinns would get stolen is that the homboi is tired of walking and the owner made it easy for them.
Most of you have such cheap bikes you could put a sign on it, "free", and it would still be there when you get back..
One good solution is to render the bike unrideable. Remove parts like the pedals is easiest. Keep the front wheel inside. Flatten the tires.
But, if you have a carbon-wonder bike then any piece or part is worth stealing, so this would not work in that case.