This is why we come to the Christian Quarter.
Seems most traffic, at least regarding tourist, comes via Jaffa Gate. Thus Christian Quarter seems the busiest.
It is choke-full of markets. Don't let this be a distractor. Move through the market, better yet around it. Or immerse yourself in it.
Besides, the Christian Quarter holds Christ's Tomb and most of the Stations of the Cross.
Tip 1: Resist the urge to continue into the Christian Quarter via the obvious path, the path choke-full of vendors. Go another route to the sites.
Tip 2: Enter via the New Gate and avoid the shock of Jaffa Gate. The New Gate will feel like your own private entrance. You can just as easily locate the extraordinary sites mentioned above from the New Gate.