Unless you have an onward ticket and will definitely only spend the hours of darkness in Lanzhou, it's worthwhile making the effort to relocate to another area of town.
Here is a Tripadvisor map of hotels in Lanzhou to get you started. You don't have to go too far to enjoy the benefits of being away from the station. The Ningwozhuang Hotel (#1) and Cuiying Hotel (#11) get good reviews, and are both within a few km of the station.
Arriving by airport bus
If you arrive into the city on the airport bus, there are several hotels to choose from within a few minutes walk (#6, 2, 15, 22, 10, 3, 13, 4). It's a nicer environment than the station, certainly, although still quite far from anywhere of interest.
Recommended Areas - Zhōngshān Lù (中山路) or Zhāngyē Lù (张掖路)
The Yashi Hotel is in a great location to explore some of the main sights (and it's on the route of the Half-Day Walk). In fact, there are several hotels on Zhongshan Lu and Zhangye Lu (which is a pedestrianised shopping street). Bus #34 gets you there (or approx 11 yuan by taxi).
Lanzhou Huar Youth Hostel
Lánzhōu Huā'er Guójì Qīngnián Lǚshě
Lanzhou 'Huar' International Youth Hostel
Lánzhōu shì chéngguān qū duàn jiā tān lù 704 hào lánzhōu wénhuà chuàngyì chǎnyè yuán D qū
Zone D, Lanzhou Creative Industry Park, 704 Duan Jia Tan Road
Getting there: Bus route from the railway station, more detailed instructions here (select the 'location and map' tab)
More information: here, here, and here
Cost: 35 RMB a night, according to this blog post (with photos).
This hostel is located in the east of the city, a bit out of the way of any of the sights listed here, but it looks to be quite traveller-friendly (dorm rooms and doubles, as well as a library, internet, etc). Apparently a new art district has sprung up there, which might be worth checking out...
View Lanzhou 兰州 in a larger map
Update (Oct 2011): Not accepting foreigners at the moment. It certainly has done in the past, so worth checking in advance to see what the current policy is.
Chinese: 雅仕宾馆 (Yăshì Bīnguăn）
Address: 299 Zhōngshān Lù (中山路 299号), a few minutes walk from the river at Zhongshan Bridge (中山桥). Map.
Buses: from the station (#34, #9, #6) or from the airport bus drop-off (#34, #127, #4)
Double room: 158 yuan (after asking for a discount)
Being so close to Zhongshan Bridge (中山桥), it is probably the best place to get the most out of a short trip to Lanzhou.
The south bank riverside parks go in both directions from the bridge, and White Pagoda Hill Park (白塔山公园 báităshān gōngyuán) is directly opposite, on the north bank. Also, Zhāngyē Lù pedestrian shopping street (张掖路步行街, for Huang Miao) is 200m to the south
Address: 天水中路20号 (20 Tiānshuǐ Zhōnglù)
Buses: #16 from the station (2km, 4 stops).
Map, and review.
Address: 天水南路226号 226 Tiānshuǐ Nánlù
Buses # 10, 16, 127, 110, 7, 1, 131 go there from the station (about 1km, 2 stops).
Ctrip prices and booking
This hotel is next door to Lanzhou University, about 1 km north of the railway station, and right across the road from the airport bus drop off.The standard room is listed as Y380, but they offered Y280, and it's probably even less if you book through Ctrip. Travelers frequently complain that the hotels by the train station in Lanzhou aren't taking in foreigners, so this seems to be a good alternative. There is also a pleasant cafe on the first floor.
Grand Soluxe Hotel - Sunshine Plaza
Chinese: 阳光大酒店 (yángguāng dàjiǔdiàn)
Address: Qìngyáng Lù (庆阳路). Map.
Buses: From the station (#34, #31, #102), from the airport bus drop-off (#1, #82, #127)
I haven't stayed there, but it looks pretty nice, and it's in a reasonable location. See their website for more details. TripAdviser reviews.
Lanzhou Wanlin Youth Hostel
See the China YHA website. Located on Ānxī Lù (安西路) in Qīlĭ Hé district (七里河区). See this map. And this one.
Buses: from the station (#6).
The hostel is reviewed here.
I can't vouch for it, but I did have a wander around and spoke to the manager. The main reception area is in the 'Wanlin Ecology Garden' (万麟生态园, Wànlín Shēngtài Yuán). Seemed like a peaceful and relaxing place. Rooms are in an adjacent apartment block.
The river is 5 mins walk to the north, and if you head east (towards Zhōngshān Qiáo 中山桥), you'll pass through the riverside parks where I recorded these performances.