Chengdu is at the edge of the Sichuan Province, so it's not far from the mountains. A short flight to the north (or 1.5 days by road) are the world-class national parks of Huanglong and Jiuzhaigou. [Unfortunately, it also has super world-class crowds in the summer, and is mostly inaccessible in winter.]

Closer by, beside the Erlong Panda Reserve Center, there is the Qingcheng Shan (Shan = mountain) area, which is more or less the same direction. Day trip material.

Towards the Southwest, there's the Leshan giant buddha and then Ermei Shan. Good for a two-night trip.

And of course, most flights going to Lhasa still departs from Chengdu, so many who go to Tibet stop at Chengdu first.