Línxià (临夏) is around 2 hours south of Lanzhou, on the way to Xiàhé (夏河). Buses from the South Bus Station, see map.
Things to do: A great place to break up the journey between Lanzhou and Xiahe. Linxia is a Hui Autonomous Prefecture, and there is a strong Islamic identity to the town. There are mosques on most streets, and plenty of Hui street food vendors at night (all manner of barbequed lamb). Wànshòushān Gōngyuán (万寿山公园), has a buddhist temple and a hilltop pagoda where you can get good views of the city's numerous minarets.
Places to stay: Linxia Hotel (临夏饭店 Línxià Fàndiàn, 红园路 Hóngyuán Lù) is modern and clean, but rooms are around RMB150-200. Budget rooms can be found in the hotel on the big roundabout between Tuánjié Lù (团结路) and Mínzú Lù (民族路), seen in the first photo below.
More information:Wikipedia (includes a good section on the mosques there).