The former residence of the Dalai Lama (1645-1959), the Potala Palace is a beautiful, sprawling, 13-level structure that sits atop Marpo Ri ("The Red Hill") in the Tibetan capital of Lhasa. With a total height of about a thousand feet above the valley below, the Potala Palace is a spectacle to behold, consisting of the White Palace, where the Dalai Lama once lived, and the Red Palace, home to a few hundred thousand(!) Buddhist shrines and statues meant for worship. Nowadays, the palace serves mainly as a museum of Tibetan artifacts where you can see ancient murals, wander courtyards and chapels, and even make your pilgrimage to the entombed 13th Dalai Lama. Tickets can be purchased through tours or individually, although numbers are limited daily. If anything, at least join the flocks of tourists below the palace and snap a picture of one of the Buddhist world's greatest landmarks.
Check the included website for prices, which change seasonally, and more information.