Nechung Monastery [free entry] lies a couple of minutes' walk down the hill from Drepung Monastery and is worth visiting. It's much the smallest and most personal of these monasteries easily accessible from Lhasa, and is the least visited, and therefore the most peaceful. Also, it is the only monastery where one may take photos freely. Historically its importance is that until 1959 it was the monastery of the State Oracle. For this reason the imagery painted on the walls is more than usually fierce and bloody [flayed human skins and souls in torment]. Nechung was greatly damaged during the cultural revolution, but is quickly being restored.

How to get there: The Monastery is close to Drepung which can be visited either as part of your "tour" from Lhasa or independently by minibus from Lhasa.
Opening hours: Daily 9am-4pm