I lived in Jordan, Amman, for 5 years. I can say that it is not safe for a woman to walk around alone, in Jordan.
Jordan seems safe but just if you are not alone. It happened several situations where I was harassed by men. Even though I was totally covered.
Every time I was out with my husband I felt very safe, even when I was with another woman out. But when I was out alone during daytime, I didn't fell safe, in different situations. I will give some examples.
I walked to the gym, wearing jeans, shirt, jacket and sneakers and I was followed very closely, by a man, always trying to make eye contact and smiling to me. Why would he follow and try to approach me for so long, seeing that I was not reciprocating and I was not comfortable.
Another day, on my way back from the gym, a taxi driver was following me and was constantly beeping the car horn. He was not trying to catch a client. I lived in Jordan for 5 years I would know if this was a normal behaviour of taxi drivers, in Jordan.
Both situations happened, in areas, where there was not people around.
Once, I went to a Middle Class shopping mall, I was wearing a black sweater, a black and white skirt, black leggings and sneakers. As I as walking, many men were staring, turning heads and making loud comments. This happened everywhere I walked! I felt naked. Like I was doing something wrong. I wanted to runaway. This was very impressive to me, because I went there many times with my husband and I always felt in a safe place.
I will mention one more. There was this supermarket next to the apartment we were living in. This was a family business. Everybody there knew us. They had a good relationship with my husband. But, when I was going alone, one of the older man used to make more personal conversations, smiling a lot with me and touching my hands. I was always dressed covered.
These are just a few situations. I just walked away quickly from these situations. But, if I smiled back, showed any friendly reaction, or if I didn't leave quickly something could have happened.
I believe that not all male Jordanians are harassing women, but many would do if there is an opportunity.
I don't have a look that stands out. I am a brunet with olive skin tone, in my late thirties. Blondes stand out for the Jordanian culture.
In Jordan, avoid to go out alone if you are a female. For men and women accompanied, Jordan is very safe. But not for a woman alone.