if the “other traffic” are solely bikes and people on foot, it can be done. If you share the road with automobiles, buses, etc., well – it is possible to survive (if you are a married male, perhaps you can arrange for a “get al tanai” in case you end up in a coma).
Follow the safety rules for cyclists. If there is a bike lane, use it. Wear a helmet and ride with traffic not against it. The nyc. gov website does have a pdf from the DOT listing the rules for bicyclists.
Biking on an urban street, even with a helmet, is extremely dangerous. WHAT IS A “fender bender” if you in a car, is probably hospitalization (or worse) if you are on a bicycle. If a city has true dedicated bike lanes (meaning bikes only, with a barrier between bikes and cars) it would be fine – but those typically are “bike trails”.
It depends which City. I biked to school and work for 30 years in Brooklyn (mostly just Boro Park and Flatbush), but now I work in Manhattan. Every day I cringe at how dangerous the bike traffic seems to be, both to the riders and pedestrians. There seems to be no safe path that they can ride on, having to weave around taxis, trucks, and stopped cars all over. I take the subway.