Originally Posted by
sinoflyer
At other times of the day, I too would prefer Beihai and Houhai over Jingshan, but IIRC Beihai and Houhai only come to life in the afternoon and really get happening in the evening. Since OP should begin returning to the airport by 10 am, there won't be many breakfast options in their vicinity, at least ones that IMO stand out and are worthy of exploring.
Jingshan seems bland, but it harbors rich culture and history if one seeks them. Many Beijingers go there in the morning to dance, exercise, and blow off steam by screaming at the top of their lungs in virtual-anonymity. Jingshan was also where the Ming Dynasty ended (1644), when the last emperor hanged himself on a tree during a peasant rebellion. A replica of that tree stands somewhere in the park, overlooking the Forbidden City and perhaps representing a cold reminder to both the governing and the governed that Chinese history tends to repeat itself.
I agree that the 4a arrival makes things a bit challenging. My initial thought was head straight to Tiananmen Square for the flag raising ceremony, but the problem with this plan is that Palace Museum doesn't open until 830a, and there's not really anything else to "do" in that area during the early morning.