Let us start by asking you this question, How safe is the Biggest City in your Country at night for Women?
Our answer to the question above would probably match yours.
One has to keep her guard at all times, no matter where you are and what you are doing; this is the general rule and should be for any traveller.
Western tourist women, in particular, catch the eyes of the man in Turkey; therefore, you may experience somewhat overwhelming attention towards yourself.
Remember that cultural differences can sometimes be good for one whilst bad for the other; therefore, do your homework before you travel to Turkey, which may help you read some hidden signs.
Remember this, every woman, who experienced something terrible during her travel, is because She trusted; she believed in that person who turned out to be her nightmare, if not the worst.