Shuttle bus from Capital Airport to Shijia Hutong,Meishi Street,Xicheng,Beijing please.

I will be arriving at Terminal 2 at about 12.00pm midnight. I plan to go to my hotel in Hutong at about 7.00am. How should I start my travel from the Airport to the hotel?.What I have in mind is to take a shuttle bus to the West Railway Station and from there I will take a taxi
to the hotel. Could anyone suggest a better option? Thank you.