Chengdu/Tibet - I've only got a week

There is definitely no need for you to begin your tour in Chengdu. Whoever told you that information is completely wrong. You can begin your journey to Tibet from just about anywhere in China. Tibet, according to the Chinese government, is an autonomous region and does not have a "border crossing" like there is going into Hong Kong, Macau or like when crossing into a foreign country. When taking the train to Lhasa, you will never know you have crossed from Qinghai into the Tibet Autonomous Region as there is no "border crossing" there.

another suggested itinerary
Day 1, arrive at Chengdu.
Day 2, fly from Chengdu to Lhasa, transfer to Tsedang
Day 3, Visit Samye monastery and Yumbulakang Palace
Day 4, Tsedang drive to Gyangtse, then Shigatse
Day 5, Shigatse to lhasa
Day 6, Lhasa
Day 7, lhasa to Shanghai??

Thanks everyone - i found a pre-arranged tour i can slot into which seems to visit the places i am keen to see for my first trip! Thanks for your help - will let you know if the tour company is worth recommending when i get back!

Cheers