This small but significant monastery and ruined dzong (fort) is just north of Lhatse in the village of Lhatse Chöde. Home to 75 monks, the monastery was built during the 17th century and there are some beautiful original murals lining the main assembly hall, where there is also a statue of the fifth Dalai Lama. Also in the main hall, look out for the black-and-white photo of the monastery and dzong taken before it was destroyed during the Cultural Revolution.
To reach the village, head 1km east of Lhatse on the Friendship Hwy to the 5052km mark and then turn north for about 15km. This road continues for 61km to Phuntsoling Monastery, and you'll pass the small Drampa Gyang Temple on your right just after the turn-off.
You need to have the actual monastery name listed on your permits to avoid a run-in with the overly sensitive local PSB. Otherwise it's not worth the inevitable hassle.