Bai'an Department Store Supermarket (basement) 百安购物 (Băi'ān Gòuwù) Nánguān Shízì 南关什字 Map
It's where I get my Yunnan coffee (update: you can often find Lavazza coffee there, sometimes at a good discount). While Parkson has the widest selection of imported alcohol, tea and coffee, Bai'an has much more of what you'd need for some western cooking (pastas, sauces, spices, olives, cheese etc).
Ya'ou Department Store Supermarket (basement) 亚欧商厦 (Yà'ōu Shāngshà) Xīguān Shízì 西关什字 Map
RT - Mart 大润发 (Dàrùnfā) 雁滩路 Yàntān Lù (Bus #20 from Anning District (via city centre) terminates here, or #53 from Xizhan) Map Wide selection of imported wine and spirits. Best value in Lanzhou for cheese.
Chinese-Korean Fashion Shopping 中韩时尚购物 (Zhōng Hán Shíshàng Gòuwù) Shuāngchéngmén, Qìngyáng Lù, East of Yŏngchāng Lù intersection, opposite Gome electronics 双城门，庆阳路，永昌南路口东边，国美电器对面 Map Coffee beans and coffee-makers.
Jiuxin (cafe & bar equipment) 久心 (Jiŭxīn) 89 Gāolán Lù (walk south from the Square's south exit, cross over Gānnán Lù, it's on the right) 皋兰路89号 (东方红广场南口往南走，过甘南路，在右边) Map Large selection of coffee beans and coffee-makers (such as these)