Lanzhou University Science and Technology Plaza 兰大科技广场 (Lándà Kējì Guăngchăng) Dōnggāng Xīlù & Tiānshuì Lù crossing 东岗西路天水路口 Map
Computers, software, MP3s, cameras etc (including authorised Apple resellers on the 2nd floor).
UPDATE: Now expanded into the neighbouring building, to the east. And, if you continue to walk east, you will come across several more, smaller electronics retailers before you get to the 'Electronics Trade City' (see below).
Walk north from the Square's Xīkŏu west gate (西口), and you'll come across a concentration of mobile phone shops, for an entire block. For SIM card contracts, go to the China Mobile on the NE corner of Xikou (map).