Lhasa

Lhasa needs 3 days: the Potala Palace, the former residence of the Dalai Lama over 3,700 meters above sea level, on one, the Jokhang Temple and the Barkhor pilgrimage circuit around it, on another, and Sera Monastery, with its famous outdoor monk debates, on the third. April-October avoids the extreme cold of the highland winter. It's mid-priced, though it requires a special travel permit for foreigners, arranged through an authorized agency. It's one of the highest-altitude inhabited cities in the world, and its Potala, with 13 floors and over a thousand rooms, was for centuries the center of Tibetan political and spiritual power until 1959.