I am flying to Beijing and my flight will reach at 23.30, so I am planning to book a hotel nearby.

The two spots you mentioned are very popular and require much time to visit. It is best to spare them in two days.

If you stay near Capital Airport, take shuttle bus line 13 to Jinyu Hutong, then the distance to the Forbidden City is within 0.8mi. Or take Airport Express Line to Dongzhimen, where you can change to subway line 2 to Jianguomen. Then transfer to line 1 and get off at Tiananmen East. Leave from exit A and walk to the Forbidden City.

To head for Badaling, you may go to Deshengmen and take bus no. 877. It will directly lead you to the wall within 70-80min.

If taking a taxi from airport to the wall, it costs CNY250 or so. To the Forbidden City, the fare can be CNY100 or around.