from Capital Airport to grand skylight catic hotel

Take shuttle bus line 5 and get off at Asian Games Village . Then your hotel is around 07mi away. You can take a taxi to reach exactly.

Do you mean that you wanna go to the Forbidden City from the airport? If so, I suggest you take shuttle bus line 1 and get off at Dabeiyao (Guomao Bridge). Then walk to Guomao metro station to take local subway line 1 to Tiananmen East. Afterwards, you can easily walk to your destination.