Why go
Use the Old City for closely spaced religious landmarks and West Jerusalem for a modern commercial center. The German Colony offers a street-focused food stop, while Ein Kerem trades the dense center for hills, galleries and churches linked to John the Baptist. Me'a Shearim calls for especially respectful dress and behavior because it is a residential religious community.
The full story
Begin with the Old City if your main interest is Jerusalem's sacred geography. Its walls and quarters give a clear framework for visiting sites important to Jews, Christians and Muslims. West Jerusalem has a different rhythm, with commercial streets and a wider range of modern city services. South of the center, the German Colony is a useful place to pause around its streets and eating spots. Me'a Shearim is largely an ultra-Orthodox Jewish neighborhood; treat its streets as a residential area rather than an attraction and dress modestly. Ein Kerem has a village character on Jerusalem's western side, with hills, art spaces and churches associated with the traditional birthplace of John the Baptist. Talpiot, farther south, is chiefly a commercial and industrial district. These places do not form a single short walking circuit. Pick a neighborhood according to the experience you want, then pair nearby stops rather than trying to cross the city repeatedly.