Hi, I have around a 10 hour layover at Beijing Capital Airport arriving at around 7am.

The fastest and cheapest way is: first take the airport express at T2 and get off at Dongzhimen. Then take the metro line 2 inner ring and get off at Jianguomen where to transfer to the metro line 1 and get off at West Tian’anmen. Then walk about 16 minutes to the Forbidden City. The whole ride needs about 70 minutes and costs about CNY30.