Kham and Amdo are both spoken in Qinghai. Kham is spoken in Yushu, which is larger than the nation of Nepal. Amdo is spoken elsewhere in Qinghai, i.e.,. Golok, Haibei, Hainan, Huangnan, and Haixi, as well as by more than 100,000 Tibetans in Haidong Region. You could enroll in either Qinghai Nationalities University or Qinghai Teachers University. The quality of the instruction is pretty much up to you, and you can always English speaking Tibetan tutors who will teach you as you as many hours as you are willing to pay for. There is a growing corpus of Amdo Tibetan teaching materials, e.g., go to uztranslations and search for /Tibetan/ and you'll find all sorts of things. If you wanted to learn Central Tibetan in Qinghai, it would be more difficult, because few speak it. The key question is what your purposes are in learning oral Tibetan. There is on /standard/ oral Tibetan--about the best you can do in that regard is a herder's dialect, and there are plenty of students in Xining that speak the nomad dialect. More than 90% of the Tibetans in the world live in China consequently, it makes sense to learn Tibetan there, if you want to live in China. The exile contention that Tibetans in China do not speak /proper/ Tibetan is as delusional and hurtful as saying that there are no "real" Tibetans lefft in China. If you plan on being mostly in the exile community, then by all means go to wherever they are, particularly India, and learn their Hindi-flavored speech--you also won't find many younger Tibetans in the exile community who have much competence in written Tibetan.
Thanks for the info! The standard of oral Tibetan outside of monasteries and nomadic camps has probably declined in all communities due to influence from majority languages. I am actually more interested in Classical Tibetan but learning a colloquial language would help in receiving teachings orally too and it seems that it is mostly in Sichuan and Qinghai that there are some gars set up which are outside of the government controlled monasteries so perhaps Kham or Amdo would be more useful there. Amdo seems to be closer to the written language.