Shigatse, Tibet’s second city, is the traditional seat of the Panchen Lama, the highest ranking lama after the Dalai Lama. Pilgrims pour through the town to worship at the stately Tashilunpo Monastery at its western end, which holds some of the most sumptuous chapels and Buddhist art outside Lhasa. Should you wish, your guide will be able to lead you along the 2-mile Kora circuit of Tashilunpo, which follows the walls and low hills around the complex and yields fine views over Shigatse Dzong (fort).