Rule #0. Murphy's law. Anything that can go wrong, will go wrong. Watch out for what you can't see. Look for potholes and traffic at all times. Look for ruts that your front wheel can get railroaded into (they can be hard to spot in low light).
Rule #1. Ride very far from car doors. That means not in the bike lane: maybe on the furthest white line of the bike lane. That leads to:
Rule #2. Don't let honking horns allow you to make less safe choices: command the space around you. It's your lane. The bike lane is for bicycles going 5mph, parked cars, and people looking to jay-walk. That leads to:
Rule #3. Stay away from the edge of the street. Shit happens there. Cars turn in front of you, and pedestrians step out by surprise, like pigeons walking without any obvious direction. The middle lanes are best. The speed limit imposed by Bill de Blasio for nyc is 25mph, if you can do 15mph, go ahead and take a lane. With traffic being so backed up most of the time, you'll be passing between the cars.
Rule #4. Be aware that, to the average driver, you don't exist, when you are on the passenger side of their car.
Rule #5. It's usually not worth drafting vehicles, because by the time you move into position, they'll be stopping at a red light. West side highway is one exception.
Rule #6. Pedestrians on their cell phones are the best. As long as they don't see you, they will walk predictably forward, and not do a dance for you. Older pedestrians in Chinatown are the best: they know their shit. There is lots more bicycle traffic in China, and they don't freak out because you are on a bicycle.
Rule #7. Don't take the Brooklyn Bridge, unless you are feeling suicidal. There be tourists.
Rule #8. Think twice before informing a pedestrian or another cyclist, that you are about to pass them. Rather than hear what you say, they will be startled and act unpredictably. It is often better to try for a stealth approach. Only with seasoned cyclists, while in a peloton, does the courtesy apply safely.
Rule #9. Plan your route beforehand, so you know which direction the one-way streets flow. If you have to bicycle the wrong way, take the middle of the street unless traffic approaches. You have more options from the middle of the street.
Rule #10. The new bike lanes separated from the car lanes by car parking, are like the trenches of the Death Star. Pedestrians will be standing in the path waiting for their light to turn green. You'll have to use your proton torpedoes.
Note #0. An example of Rule #0. What could be the safest bike lanes of all, such as the one next to the West Side Highway, have “safety” signs and concrete separators right in the middle of the path. You could easily run into one if you are distracted, which is easy to do considering the perceived safety of being in a dedicated bike lane. Most likely they were placed there by non-cyclists. The barriers were placed after a 2017 truck attack, to keep vehicles off the sidewalk. Once again terrorism wins, because those wanting to make things safe ruin everything. Remember how much nicer things were before the TSA at airports?