People’s Park & Heming Teahouse → Kuanzhai Alleys → Kuixinglou Street → Chunxi Road & the IFS panda

This is the day Chengdu explains itself. Start in People’s Park at the Heming Teahouse — nearly a century old, the city’s most beloved spot for a covered-bowl (gaiwan) tea, a newspaper, and the local institution of a professional ear-cleaning. Nothing captures Chengdu’s famous unhurriedness better. Walk to the Kuanzhai Alleys, then the food-famous Kuixinglou Street (get there early for the skewer joints — the queues are real), and end at Chunxi Road, the downtown shopping heart, where the IFS mall has the giant panda sculpture clambering over its roof (go up to the 9th-floor terrace for its face and the night view).

Jinsha Site Museum → Du Fu Thatched Cottage → Qingyang Palace → Taikoo Li & Sino-Ocean bookstore (evening)

The deeper city. The Jinsha Site Museum displays the 3,000-year-old Bronze/Shang-era civilisation unearthed here — the Golden Sun Bird emblem is its treasure and now the symbol of Chengdu. The Du Fu Thatched Cottage, where China’s greatest poet lived in exile, is a green, quiet literary shrine. Qingyang Palace is the city’s oldest Taoist temple. Close in the contemporary city: Sino-Ocean Taikoo Li, the open-plan luxury-and-lifestyle quarter beside the Daci Temple, with the Fangsuo and Cat’s Sky City bookstores for a calm hour.

Dujiangyan Irrigation System → Mount Qingcheng

An easy high-speed-rail day trip west. Dujiangyan is the 2,200-year-old irrigation system still watering the Chengdu plain today — a genuine feat of engineering, best understood with a guide (the Fish Mouth, Flying Sand Weir and Bottle-Neck Channel are the working parts). Nearby Mount Qingcheng, cradle of Taoism and "the most secluded mountain under heaven," is a cool, green, temple-dotted climb (front mountain for temples, back mountain for scenery). Both reachable by the fast train from central Chengdu in under an hour.