There is a zipline about 200 metres west of the back gate at the top White Pagoda Hill Park (白塔山). There are photos below, and a promo video on Tudou (which is pretty good, if you can ignore the 'busy' webpage). You can also do a zipline at Xinglong Shan (no photos).
The Waterside Mosque and White Pagoda Hill, photographed from the south side of the Yellow River. The new hillside development is the Lanzhou 'Golden City Pass' Customs and Culture Quarter, home to the China Qinqiang Opera Museum.
More historical photos here.
steles here are stone tablets carved with poetry and calligraphy (in a variety of styles), related to life in the northwest of China. If you can't read Chinese you probably won't get much out of it. That said, the gardens are pleasant, and it's an impressive building, with a fantastic view of the city on a fine day. (兰州碑林 Lánzhōu Bēilín) is perched on top of the hills on the north side of the Yellow River. Entrance is free, if you bring ID. For some reason this is very important to the people at the gate, who were very reluctant to let us in last time we were there without ID. The
Getting there: You can walk up (via White Pagoda Mountain) or take the chairlift from the south side of the river. See the half-day walk.
Thanks to simatani for letting me use this photo of Lanzhou city centre, taken in 1994. I've tried to recreate it below.
There is a route up Baita Shan that takes you along the perimeter of the park itself, and brings you out on the road behind. Look for the steps that lead up to the mosque, to the right of the park entrance. As you climb, Chaoyang Shan is the hillside to the east. Map here.