I am arriving at 1:00 am at Beijing Capital Airport.

Well, according to your arrival time, maybe you can catch the shuttle bus Xidan Night Line. Take it and get off at Main Railway Station first. The ticket fare is CNY 24 per person. Then take a cab to the destination.
If you didn't catch the shuttle bus, you have to get a cab from the airport and directly go to your hotel. In general, it costs CNY 120-130 at night.

Thank you :-)