8 hour transit - How easy to get to Forbidden City?

According to your condition, you are advised to take the airport shuttle bus line 13 to Wangfujing Street Bus Stop. It will cost CNY25/person. Upon arrival, you are about 2 kilometers away from the Forbidden City, so you can take a taxi there at a cost of around CNY15 in the day time.
The museum will stop entering at 16:10 and close at 17:00, so you have time to make this short tour. Notably, you may book the tickets in advance.

Hi Kate, many thanks for your reply. So you feel the shuttle bus would be better than the Airport Express? How long would you think either of these options will take me, around an hour? Looks like maybe taking into account travel times to and from centre, maybe I will get as much as 4 hours at Forbidden City/the centre. Any other recommendations? Thanks.

Well, you can also take the Airport Express, and it may be faster than the shuttle bus. This route may take around 50 minutes, while the shuttle bus may take about 70 minutes.
If you don’t mind, you can also take a short trip to Summer Palace. You can take the Airport Express to Sanyuanqiao Station and then transfer metro line 10 to Haidian Huangzhuang Station. Afterwards, you may catch metro line 4 Daxing Line to Beigongmen Station, Exit D, Southwest Direction. Then you can walk about 700 meters to the Summer Palace.