No. 2 airport shuttle bus will pass Tiananmen Square and stop at Xidan Station, the first bus leaves from the airport at 07:00 am, and the last one depends on the time of the last domestic flight. See Beijing Capital Airport Shuttle Bus(https://www.travelchinaguide.com/cityguides/beijing/transportation/airport-shuttle.htm) . After you get off at Xidan Stop, you may walk east to Tiananmen Square directly or take bus No. 20. The forbidden city is right behind the Tiananmen Square.