Is there a train/subway that goes from the airport to Landmark Hotel in Chaoyang District in Beijing

If you don't mind, shuttle bus line 1 can take you to Liangmaqiao Station, which is within walking distance from your destination.

By train, you can take Express Train to Sanyuanqiao Station, where transfer to subway line 10 to get off at Liangmaqiao Station. It is within several walking distance from your hotel.

Thank you very much Jen!!