Eastern Tibet, we still call it Kham, is a land apart from the rest of Tibet. It's climate, geography, flora and fauna all lend it a unique, almost magical atmosphere. The scenery often resembles the Swiss Alps more than the high Tibetan Plateau.
It is possible to travel the northern or southern routes into or out of eastern Tibet, but to visit both, a loop route makes best sense. From Lhasa the southern route heads eastwards over a high pass ( Mila) to the gorgeous alpine lake of Draksum-tso, and then proceeds to the lovingly restored Lamaling Temple. From here the road climbs to Serkhym-la where you will have a breathtaking of Namche Barwa, and then drop down into the dramatic misty gorges that lie north of the Yarlung Tsangpo by passing Lunang forests. Take some time to visit the picturesque turquoise lake Rawok-tso nearby Pomi, then swinging north over high passes and down into the deep parallel gorges of the Salween and Mekong Rivers. Crossing the Pomda Grassland before arrival at Chamdo which is the capital of Chamdo area. Have a good rest in Chamdo after 5-6 day trip, then do a pilgrimage circumambulation at Galden Jampaling Monastery.
From Chamdo the northern route continues three days westwards to Nagqu, slowly climbing to the high-altitude pasturelands. En route you will visit the very impressive and remote Riwoche Temple and several other Buddhist and Bon Monasteries. Sok Monastery is a highlight in this area but probably you couldn't visit it even you get a permission.
From Nagqu it's a good idea to visit Namtso en route to Lhasa, though the road can be completed in a day.
A shorter and cheaper 5 to 7 day loop itinerary from Lhasa to Draksum-tso and Lamaling Temple, returning via Tsetang, visit Smaye Monastery and possibly to the holy lake of Lhamo La-tso.