Spend at least one Friday there, to experience the controlled frenzy as this holiest city in Judaism shuts down for Shabbat, starting around noon.
(Being a gentile, I never find these “days of rest” very restful.)
Book the sabbath dinner at your hotel well in advance. Only one elevator may be in service, and will stop at every floor.
In other words, think ahead about your food, transportation, and other necessities for the next 24 hours.
At the Kotel (live web cam!), modest dress is not just a suggestion. No-nonsense ladies shove raggedy shawls — NOT tallitot (that would be illegal) — and/or long, ugly aprons at visiting females showing too much cleavage or leg (or even arm).
I hate it, but I wear a long “wife-of-the-cult-leader” skirt and carry a pashmina at all times in Jerusalem anyway, and keep a kippah in my pack for my husband. When you travel with Jewish groups, as I do, spontaneous multiple visits to the Kotel are pretty much to be expected; why look like a brainless tourist with a smelly used cloth around your shoulders?
(And yes, the dress code for men is much more relaxed. Sorry.)
At the Wall, you’ll likely see bar mitzvah and wedding parties from all over the world, singing local schoolchildren, maybe newly sworn-in Israeli soldiers — it’s a Jewish Fellini movie, but reverent.
In contrast, the Christian sites in Jerusalem (and in the entire country — I’m looking at you, “Spaceship Jesus”) are mostly depressing, shabby, and grim. Too much… beige. Capernaum in particular made me think of that WW2 parody song, “How Ya Gonna Keep ‘Em Down On the Farm, After They’ve Seen the Farm?” What can I say? I’m Catholic. I need some bling.
The Church of the Holy Sepulchre alone is enough to turn anyone atheist, and not just for aesthetic reasons. For centuries, the Arab family who lives across the way have been the keepers of the keys to the Church, because the warring Christian factions who run different bits of the building can’t agree on which of them should get to keep it.
And then there’s the stupid ladder thing.