Well, the first place I suggest that you visit is the Great Wall, the longest wall in the world, which is said to be one of the wonders in the world. It has a history of more than twenty centuries. It is amazing to see such a huge wall was made entirely by hand.
The other place worth visiting is the Palace Museum, which was built in 1406. Twenty-four emperors once lived there. from there the ruling emperors issued orders. You can learn a lot about Chinese history by visiting this Palace.
What a pity that you can't stay longer, otherwise, you could visit many other historic places and beautiful scenes such as Summer Palace, Bei Hai park.. and so on.