We rode the subway while on our New York City trip.
It is an efficient way to get around, and we felt safe - though more so on the trains itself rather than at the stations. The lines are easy to understand and trains are frequent.
Our only issue came with buying tickets at the stations - as international visitors, we could not pay with card as it required a U.S. zip code. One time, a ticket didn't work either, so be wary of that.