They have tours to the countryside, but they'd be hard for foreigners to arrange or even understand, as there are few English speakers out there. A really cool tour I did was to stay in a Tibetan village in far western Sichuan. It was about four hours by car from Chengdu and really out in the middle of nowhere. The guy who ran th tour was from that village. He had left to join the army, which then sent him to university, where he married a rich girl and she bankrolled making his village into a tourist attraction. Otherwise, no one in the outside world would ever know that place existed. We slept on boards with blankets, had an outhouse, an ice cold shower and decent meals cooked for large groups. Everyone else in our group were city slicker kids from the university in Chengdu. My friend was also a student at that time and she figured I'd get a kick out of it. You really feel like you're going back 500 yrs. And I don't think you'd see anything like it from a train window.
Unfortunately, I think that village was probably destroyed in the 2008 earthquake, as it was pretty close to the epicenter and everything was made out of pretty primitive building tech.
We passed through some other cool places on the way there that seemed like modern metropolises by comparison.
The guy on the left is the guy who, with his wife, started this tour company and is from this village.
My friend told me it's not uncommon in Tibetan culture to knock on a stranger's door and offer to pay them to make you a homecooked meal for $$. That was a pretty cook experience. Really enjoyed that one - dirt floor kitchen, yak meat with some greens, rice and a beer from Chengdu. I think we paid around $3 for the both of us and I really argued to pay more, but $3 is what I was allowed to pay.