IT took five minutes into my pilgrimage for somebody to offer me free food. Leaving my inn, a converted 19th-century mansion in the Israeli town of Nazareth, I’d turned the corner to make the initial ascent toward the Franciscan Mensa Church. The church stands on the site where Christ was said to have dined with his apostles just after his resurrection. A smiling man with a lazy eye, standing by the trail head, decided I should dine, too.

He handed me a chocolate bar, gesturing toward the orange trail markers that demarcated...