Around Beijing you have many options as it is also the cultural of the country too. The main attraction is a trip to the Great Wall of China but there are many other ancient temples, tombs and palaces, as well magnificent modern sights to discover and explore. Here are few close by:
The Great Wall of China stretches cross the hills in the north of the city is about a 1 hour train ride from the center. One of the great monuments of Chinese history the Qin Dynasty started building the wall as early as 221 BC. There are 8 different sections of the wall open to visitors around Beijing, so its good to plan which section of the wall you would like to tour, to fit within your time at hand.
Ming Dynasty Tombs are 60 minutes or 42km Northwest from Beijing. This is gigantic collection of mausoleums where 13 emperors from the Ming Dynasty are buried. It is listed as a UNESCO World Heritage Site with the Scared way. Chang Tomb, Ding Tomb are Zhao Tomb accessible to visitors.
The Summer Palace is another mandatory tour. It was the sanctuary of the Qing Dynasty emperors escaping the suffocating Beijing summer. Full of temples, gardens, pavilions, bridges and corridors beneath the majestic hilltop palace and surrounded by the Kunming Lake, its 12km northwest of the city center. You will need at least a full day to explore the Court, Longevity Hill and Kunming Lake areas.
Chengde is another ancient city with a stunning summer palace, 4 hours from Beijing. It is famous for the mountain resort used by the Yongzheng and Qianlong emperors. Visitors can enjoy genuine Chinese and Tibetan architecture of another scenic UNESCO World Heritage Site.