About 3km west of the Potala Palace is the Norbulingka, the former summer residence of the Dalai Lama. The lifeless temple-like buildings rank well behind the other points of interest in and around Lhasa, since most rooms are closed to the public.
The pleasant park contains several palaces and chapels, the highlight of which is the New Summer Palace, built by the current (14th) Dalai Lama. It's debatable whether it's worth the entry fee.
The park is a great place to be during festival times and public holidays. In the seventh lunar month of every year, the Norbulingka is crowded with picnickers for the Shötun festival, when traditional Tibetan opera performances are held here.
As you leave the palace after your visit, pop into the charming yellow-walled mani lhakhang to the south of the Norbulingka entrance.