The Great Prayer Wheel of Shangri-La stands on the top of Guishan ("Tortoise Hill") above Dukezong Old Town. It is enormous — 21 metres of gilded copper, covered in prayers, mounted on a granite base — and impossible to miss; you can see it from much of the town. Push it (with the half-dozen other visitors who will inevitably be there) for three turns and you have done what you came up the hill to do.
Next to the wheel is Guishan Temple, a small but active Tibetan Buddhist shrine, and a viewing platform that takes in the whole valley: the Old Town on one side, the modern grid of new Shangri-La beyond it, and the Songzanlin hill in the distance. Come up here near sunset; it is the best view in town.