Some people use Lanzhou as a jump-of point to Xiàhé (夏河 map), or to break up the journey north up the Silk Road towards Jiāyùguān (嘉峪关) and Dūnhuáng (敦煌). Well, if you want to make the most of the opportunity to see a bit of Lanzhou, deposit your bags in the left luggage office, and do the Lanzhou Half-Day Walk. The walk takes in the main sights near the river at the Zhongshan Bridge stretch. If you have a particular interest in mosques, then try the Hualin Ping walk instead (map), which takes in the main Hui Muslim district.
If you've already covered the ideas above, head out of the city. Jiaolong Temple is about 45 minutes away by bus. Xīnglóng Shān (兴隆山), and Qīyún Shān (栖云山) are near Yúzhōng (榆中) county town, 45 km to the south-east of Lanzhou. There is also a page on overnight excursions.