Just make sure you don't wander down dark alleys when you've had too much to drink in the early morning. The crime rate is relatively low in New York City. When crime occurs, it usually doesn't take place in areas with a lot of tourists around Manhattan. For example, most tourists are unlikely to visit Harlem, the Bronx, or other districts where crime is more likely to occur.
These neighborhoods in Manhattan, between Midtown and Downtown, are very welcoming to visitors and, for that reason, are known to be easy to navigate and safe for all travelers, including women, families and people traveling alone. If you avoid them (and as you can see, none of them endanger your life), you'll avoid danger on your trip to New York and you'll be very safe all the time. Yes, it's safe to drive a car in New York, but it's highly recommended to be prepared for traffic that starts and stops, difficulties in finding parking, and high tolls on bridges and tunnels. It's especially important to be vigilant on the New York subway and, if possible, avoid taking the train late at night.
It may seem tempting to take a walk through Central Park at dusk, but it's safer to wait for the sun to rise. If you're visiting for a long weekend, a day, a week, or a month, you're likely to stay in areas that are in Manhattan or near the central parts of Manhattan, Brooklyn, or Queens, so you won't have to worry about safety at all. There are many wonderful and safe attractions for families, such as museums for children, incredible zoos such as the Bronx Zoo and the Central Park Zoo, entertainment such as the children's theater, and lots of fun restaurant and park options. There are many neighborhoods in New York where it's safer to stay in a hotel, hostel, Airbnb, or rented apartment, but honestly, it's hard to find a neighborhood that's dangerous, unless you're going very far to Brooklyn or the Bronx (I mean, very far away).
Usually, local New Yorkers don't get excited about these regular naked cowboys or superheroes. Crimes aimed at visitors are really hard to find, and that's because New York is a very safe place to be women, alone, in a group of women or in a family. Remember that “how safe New York is for tourists” doesn't matter if you ignore all the precautions, so since New York is considered one of the safest cities in the world to travel to, as a tourist in a busy and unfamiliar area, you should be careful in any city that is considered safe to visit. Airbnbs are also usually safe; keep in mind that if you choose to share an Airbnb, such as a private room, you'll be staying in the host's home and, for your safety, you should check that that person has a verified Airbnb account.