Which linguistically Tibetan areas of China are outside the official Tibet borders with the very strict permits/rules?

Tibet has very strict, difficult, and complex permits and rules. Basically most people visit as part of an organized tour group, which is not cheap and visiting as an independent backpacker is pretty much not possible, unless you have Chinese citizenship.

There are also Tibetan cultural areas that are not in the official border or zone of Tibet itself as set out by China and to which the above relates. Such areas can be freely visited like most of the rest of China, by anybody with a Chinese visa.

I believe most such areas are in Sichuan province, but I'm not really sure. Maybe also in Yunnan?

But one thing I have recently learned is that in many such areas, even when people speak their traditional language, it will be a distant relative not mutually comprehensible with Standard/Lhasa Tibetan. Probably further apart than French and Romanian in Europe.

Basically I am a language enthusiast and I want some exposure to Tibetan language. I don't care if it's a dialect, mutually comprehensible. This would still make written Tibetan usable. I want to at least learn the alphabet in a place I will see it every day.

I know a better option would be to visit Nepal or India where the Dalai Lama and many Tibetan Buddhists live in exile, but I'm probably not going to be in Nepal or India on this trip and I should be in China for at least four months.

If there is no such place, that is an acceptable answer. But please show in your answer how you know this is the case.