how do i spend my time in Beijing for 13 hours? Any sightseeing in the city centre?

During the layover, you are advised to pay a visit to the downtown area. You can go to see Tian'anmen Square, Forbidden City, South Gong and Drum Lane, and Wangfujing Pedestrian Street. You should return back to airport at least 2 hours prior to departure. If by taxi, the trip takes about 50 minutes, and the fare is around CNY 90.

If you plan to go to the Great Wall, you may charter a car or join a tour. As I know, TravelChinaGuide arranges such tours. If you are interested, you can contact them through tourstravelchinaguide.com. ;)