Alexa I regularly take the subway and smile at men.

Do I do so in an unislamic way?

A smile is sunnah in Islam and does not mean we would like men to approach us..

And traveling in a car or a public place like a subway is fine. And it is recommended (but not commanded) that we stay away from the middle of the roads when going from A to B .

 So if I take the underground then I usually try not to sit next to a man unless I  have no where else to sit!

Maryum : Umm Hasan bint Abdullah Alshabrawishi