The Wailing Wall... I do not know whether to call for a visit - it is individual for everyone. For Jews, of course, it is a shrine and you definitely need to go there. I am a tourist, I was interested from a historical point of view and I did not regret it. Before approaching the Wall, you will pass the checkpoint, then the women must cover their heads, and the men pin bales (disposable ones will be given for free). The space in front of the Wall is divided into "M" and "W", it is more spacious for men, but there are more praying women. I didn't write any notes - it's not our tradition, but I managed to get very close and put my palm on the Wall, amazingly - it's warm, like a human body. I just squeezed my eyes shut and made a wish - a year later it came true. If you are an unbeliever or you are calm about the sights, then you will be bored there. We didn't have much time that time, next time we will try to climb to the mosques. And yet - there are Garbage gates nearby, through which you can leave the city and explore other interesting places. You can also book an individual tour (but this is in Israel itself) and see the tunnels under the Wall. By the way, there are toilets near the square, but they say it's dirty (we haven't been there).
It's a good place! I advise everyone to visit! Security is well organized, politely warned that it is not advisable to do this today! Security is very tolerant and if you do not do desirable actions, then you are very politely warned about it. For example, in order to prevent terrorist attacks, you cannot use a phone near the Wailing Wall. But no one is shouting at you, there are no hostile actions, they only warn you carefully, and in their native Russian!
A wonderful historical place. I really liked the old town. Merchants accept any currency. There are many pilgrims from all over the world. At the border, if the border guards do not like something, they may not be allowed into the country.