If you want to go to the Great Wall in the morning, then you can get to see the Temple of Heaven or summer palace in the afternoon. Personally, I love the Temple of Heaven, Forbidden City. Get off the Forbidden City and get to some hutongs or bars in Shichaihai area at night. Badaling is not good as I expected. To save time, you can participate a one-day tour which offer vehicle and guide. A selection of some best Beijing package route are listed here in Beijing Tours(https://www.travelchinaguide.com/package/beijing.htm) . It may enlighten you. I missed Summer Palace last time, which is said to be a pity by many friends who have been there before.