Agree with most of the other posters here that you should have spoken up.

Totally understand your concerns being a woman and in a big city, but NYC taxis are heavily regulated here and each cab has a "medallion number" prominently displayed to passengers for many reasons but this is one of them. You are paying the fare, you get to dictate where and what they do.

If you tell them to bring you to Times Sq but on the way there you decide you rather walk or go elsewhere -- you tell them to stop and let you out at the next safest spot to pull over, and they need to stop the fare meter and comply.

If they do not comply with your instructions, they could lose their medallion if you report them.

I know hindsight is 20/20, but honestly you are definitely not the first and only woman to ride a cab alone in this city and though I'm a guy, I would have a little more faith in people instead of assuming every single man is out to take advantage of you.

If they truly did "take the scenic route" to jack up your fare, chances are it was because you exuded being a 'clueless tourist' and not because you are a woman. Still very shitty and grimey and makes us look bad as a city, but now you know for the future.