I lived there a while and sometimes visit and have my opinion on advising new visitors. They *have* improved the subway from the lowest point in the 1980s when the city virtually went bankrupt and non-funding meant that nightmare smells/non-Air conditioned/non-patrolled subway cars were the great majority. But while much fewer are that bad now, subways are not by definition a smell-friendly paradise - it's still a matter of luck what you get. Or who you get squeezed against, if you have to ride them during commuter rush hours. Ah, memories of Mystery Subway Smells during Summer Heat...
As to safety, I have two controversial chief suggestions for first-timers, which kept me alive there day and way,way into the night. The overridingly more important factor is "safety in numbers." I found that even more important to whether it was day or night was the amount of surrounding foot traffic. (As smitty may recall, even in scary Harlem, inside of the 125th subway station is just fine at midnight when there are tons of people there.) There's a scale of what numbers make it safe to enter/remain on a block, with 99.99% confidence if there's an unoccupied policeman there or a crowd surrounding you, down to 0.01% when it's dark, cold, snowy, and you're not in constant eyesight of other people.
Failing that or as an adjunct is "no eye contact." It really only matters with certain types of scuzzes in certain scenarios, but unless you know when-and-when-not to apply this, the easy thing to do is never make eye contact ever (and if you slip, don't hold it on them) - just stare ahead and downward. You may have heard that New Yorkers are impersonal
- this is *their* default behavior. Hey I'm not saying that the New York insanity is "right" - this is just the strongest strategy to avoid trouble if you don't have a feel for it yet.
I'm with what Oaktree said. I'll take the subway if I'm confident, and I'll walk onto a block if I'm confident, and when not, that's the time to grab a cab.
Finally, it's not necessary, but having a native New Yorker (or experienced visitor with savvy) with you makes things far more relaxed. You don't have to always have your guard up when you have a guide. The bad guys seem to smell when one's guard is down.