Beijing Airport to Hotel Transportation: Fastest way? Cost?

If you want to use the airport express, you can take it to reach Dongzhimen Station, where you can change to subway line 2 to get to Chongwenmen Station. Then change to line 5 to reach Tiantan East Gate Station. After that you can hire a local taxi to your hotel.
The airport express charges 25RMB per person and the subway fare is around 2RMB per person. The taxi fare is around 17RMB.

Since the subway cannot take u to your hotel directly, so I suggest you to use the airport shuttle bus + taxi to your hotel. In this way, you can take the shuttle bus line 10 to reach the south railway station and then take a taxi to your hotel. from the south railway station to your hotel, there is about 3 to 3.5km. The airport shuttle bus costs about 24RMB and the taxi fare is around 15RMB.