The city museum on Mingshan Road covers the local archaeology of the Hexi Corridor: Han-dynasty silk fragments, wooden writing slips from the Yumen Pass garrisons, Tang-era ceramics, some Buddhist statuary, and several reproductions of the most important Mogao caves at full scale that you can examine up close (no Mogao guide rushes you along here). For travellers who can't get back into the actual caves for a second day, the replicas are the best alternative.
The captions are in Chinese and slightly stilted English. Allow ninety minutes; pair it with a meal at the nearby night market. Closed Mondays.