Will go to Beijing in a few months, and I have a problem: my flight arrives at Capital Airport 2 am

And my hotel is near the center of the city. How can I go to the airport to the hotel? I did not find routes available during those hours. Do you know if there's a night bus or something? How much will the taxi cost?
The hotel is located near Meishi Street to Shijia Hutong, 50 meters inside the Hutong.
谢谢 :)