You don't want to be in the old city when it gets dark. You will get lost (especially without a map). Forget about asking the way. Some people might be helpful, but most send you the wrong way!
Also watch out you get sunburnt very easily here! I burnt my head, arms and shoulders ouch! You can see my sunburnt head on the picture ;o)
Guidebooks often warn about walking through the old city at night, and I can see why. As soon as dusk descends, it can be spooky, especially if you're a solo female traveler. The narrow paths and sundry dark alcoves and alleys are tailor-made for thieves and rogues of the night. I stayed in the old city, at the Lutheran Youth Hostel, but didn't go far alone after dark; why chance it?
of course,you will not say that you are jewish when you have a walk in the arab part of the city,and you will not wear a kipa;always try to show that you are an innocent tourist