Adventure Travel
If visiting monasteries that are seldom visited is your goal, put Ralung on your list. It is a small monastery but it is said to be the location where the red-hat sect of monks was originated. That makes Ralung a very sacred location. Aside from that, Many of the ruins from the cultural revolution can still be seen. And beyond that, the monks of Ralung are some of the friendliest monks I have ever encountered. Upon my arrival, they acted as if no one had ever visited them before. The highlight of visiting Ralung is definitely the interaction with the monks.
My visit was in 2006 and it was a day trip from Lhasa. I did not have time my two subsequent trips to Tibet but I hope my next one , I will have time and a guide that will take me back.