What are the transportation options to get to Gansu from Beijing?

Oh, I unsderstand. Gansu is a province referring to a large area. Since you want to visit the Labrang Monastery and Samngke Prairie, I suggest you make a transfer in Lanzhou City.

From Beijing West Railway Station, there are trains available, and the travel time is about 18 hours. There are also many flights available, too. Upon arrival, take a taxi to the Lanzhou south bus station before to catch the bus to Xiahe. Upon arrival in Xiahe, where the Labrang Monastery is located.

The Sangke Prairie is located about 9 miles from the county, you can take a taxi at a cost of around CNY30-40. Or you may rent a bike to ride southwest along the main road to the Sangke Prairie.

Thanks, Sarah!
And do you suggest any other sites nearby worthy visiting?

Oh, yes, there are also other popular scenic areas near Lanzhou, including Waterwheel Garden, White Pagoda Park, Five Springs Mountain Park and the Provincial Museum. Hope helpful!