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.