Although religious centres have existed in the region since around the 8th century, Rongphu Monastery (4980m) is now the main Buddhist centre in the valley. While not of great antiquity, Rongphu can at least lay claim to being the highest monastery in Tibet and, thus, the world. It's worth walking the short kora path around the monastery's exterior walls. The monastery and its large chörten make for a superb photograph with Everest casting her head skyward in the background.
Rongphu was established with the name Dongnga Chöling in 1902 by the Nyingmapa lama Tsedru Ngawan Tenzin. It has traditionally coordinated the activities of around a dozen smaller religious institutions, all of which are now ruined. Renovation work has been ongoing since 1983, and some of the interior murals are superb. Upstairs is a large statue of Guru Rinpoche.
For a great hike, you might be able to follow the walking trail south from the monastery for 30 minutes to the ruins of Rong Chong, Rongphu's former meditation retreat. The route passes a ruined nunnery, which is still home to a couple of nuns in retreat. If in doubt about the way, follow the electricity poles. Below the ruins, next to the road, is a set of springs. As this is a sensitive border area, check with your guide (who may check with local officials or insisting on accompanying you) before setting off.