Drepung Monastery sits in the foothills above Lhasa Valley. The Kora offers amazing views of Lhasa Valley as well as the wetlands on the outskirts of the city. Along the Kora you will find several stupas for incense offerings, usually burning well. Much of the Kora is a stone walkway around the outside of the monastery.
At the very back of the monastery, look for a bridge on the left. Below the bridge is a sacred spring where local Tibetans fill jugs with water. There is a short trail that works up a small hill with prayer wheels scattered about, turn as the wind blows through the trees.
Near the end of the Kora you will see the ruins of the original monastery. This section was destroyed by the Chinese during the Cultural Revolution. It is common for the Monks not to rebuild on the exact spot of the destruction.
I recommend walking the Kora first and then exploring the monastery when you are through. It should only take about one hour or a little more.