Hi.
I traveled to Turkey last year. I loved it and would like to return some day. I felt safe, taking the usual precautions of course.
I was regularly harassed, however, in Istanbul....and not just by carpet salesmen. I had 3 separate incidents where men "tailed" me. One time I was harassed to such an extent that the next day a Turkish man (and a young Canadian girl who was only allowed to visit turkey while escorted by him) came up to me and said "your that girl that was being harassed". I am beyond my 20's, not flashy, generally don't wear makeup, plump...., so I did not expect such constant attention. It was quite a pain-in-the-butt, and at one point I wondered why I went there.
That said, I think it is safe and I want to return to Turkey (more so the countryside) at some point. I was traveling solo and maybe that was part of it. (I would not want my nieces to travel there alone). But I would recommend you be more "stand-off-ish"...maybe drop the quick smile and greetings that most of us use casually...even blatantly ignore people and just go about your sightseeing to avoid the harassment while in Istanbul. And take the usual precautions of being aware of your surroundings.