Traveling with a friend in mid Dec. Public transport from city centre

To Mutianyu: You can take subway line 2 to Dongzhimen first. Then take bus line 916 Express to Huairou North Avenue Station. The 916 Express costs CNY 12 and takes 60-70 minutes. After arriving, take a minivan to the scenic area with the fare of CNY 50-60.

To Badaling: Take bus no.877 from Deshengmen and get off a bus stop which close to the pulley car lower station and about 10 minutes' walk to the entrance. It takes about an hour and costing CNY 12 per person.

Thanks! Any suggestions for places to visit in Beijing?

If you have enough time, Forbidden City, Tiananmen Square, Summer Palace, Wangfujing Street and Hutongs are strongly recommended. :)