Just a suggestion:

Dunno the time of the sunrise on the day that you arrive in Beijing, but IMO catching a rear view of the Imperial Palace from the peak at Jingshan Park is worth considering. Also, I dunno when the first Airport Express leaves from PEK T3 or T2 to make this feasible. Regardless, once exiting the Airport Express at Dongzhimen, hire a taxi to get to Jingshan.



Next to Jingshan Park is Beihai Park. If you walk there from Jingshan, you will see the watchtower on the northwest corner of the Imperial Palace complex that occasionally appears in print advertisements in the West.



And if traditional Beijing style breakfast interests you, Huguosi (Huguo Temple) Street a couple of blocks northwest of Beihai Park has many eateries, including the old-school Huguo Temple Snack Shop that still operates like a state-owned canteen. (E.g., Exchange cash for paper coupons at the cashier, and then use the coupons to exchange for the snack dishes that you want to try. Redeem unused coupons back to cash afterward.)