We had a great time at Shilingxia Gorge (RMB68, opens 7:30am) and the UFO glass platform (RMB40) during a cool sunny day.
You can take the 2hr bus journey from Beijing or stay at the many simple village accommodations near the Gorge entrance so that you could start your day early to visit Shilinxia, Jindong Karst Caves and Tianyun mountain (with another glass bridge) all in the vincinity.
We decided to trek up along the stream (all paved paths), taking in the beautiful sights along the way. There was a direct stairway route up to the glass platform from the entrance but I imagine it would be quite a torturous climb and missing out a bigger part of the beautiful gorge. We spent about 4 1/2 hours there (leisurely, without cable car).
You can choose to take the cable car up (RMB100 each way). However, it would only bring you about 3/4 way up the mountain and one would still need to climb flights of stairs the rest of the way up.
Getting there by bus:
If you are versed in the Chinese language, you could download the 高德地图 or Baidu map app (Chinese equivalent to Google map, with get clear instructions how to get to your destinations.
From Beijing, go to the Dongzhimen subway station and follow the signs to the "bus transfer hall" (Long-Distance BusHub). Take bus 852 (RMB15) to Pinggu district (1hr15m). Alight at Pinggu Hospital or any stop along this road. Then take either bus 25 or 38 to Shilinxia 石林峡 (RMB5, 40min). Buses and routes are all listed on the bus-stops (in Chinese).