I grew up riding back roads but you couldn't pay me to ride a bike in a city, at least not in commuter traffic anyways. I don't care how diligent or alert you are as a rider, the stats are stacked against you.
I think riding in NYC is a lot safer then the suburbs. Just follow the golden rules:
1. Avoid Uber/Lyft drivers because they are absolute morons and are clueless where they are going.
2. Reduce speed where there are a lot of pedestrians.
3. Avoid the BQE during rush hour.
(all apply to cars too!)
Now that we reduced your likelihood of crashing. Lets talk about the off chance that you do crash:
The speed limit in NYC is 25 mph. And there aren't many places that you can go much faster then that. A crash at that speed is unlikely to be fatal or result in terrible injuries. Most drivers here are service workers, taxis, or commuting to work. These people generally are attentive drivers because they are one traffic ticket away from losing their license.
Lets talk about the suburbs. The suburbs of NYC are really scary. There are soccer moms piloting their 50-70 mph missile on roads with pedestrians, all while doing their make up, reaching for the kids in the back seat, and replying to a text message. This is 90% of the roads that you will travel on. Good luck if little Jimmy in the backseat is tossing animal crackers and mommy isn't paying attention that you stopped for that red light.