If Tibet won't work out you might consider going to Deqin (NW corner of Yunnan on Tibet border). You can go there with no permits and there is some good trekking in the area, spectacular scenery (especially if the weather is right), and friendly people. And it is very Tibetan if that is what you are after. One of the main treks in the area is the Kawa Gebo pilgrimage.

There is a guy (British I think) who has set up a trekking lodge up there and has gathered a great deal of relevant info. I visited his lodge the last time I was up there.

http://www.deqinlodge.com/page/page/6855278.htm