You don't say if you have ever visited before. Presuming this is your first visit then it would seem best use of your time to visit a section of the Great Wall (Mutianyu is a good compromise) on one day and this could be combined with somewhere like the 798 Art Zone if you have an interest in contemporary works. Otherwise, maybe return to the city and visit the Summer Palace as this is on the outskirts. The other day culd then focus on Tiananmen Square and Gate and the Forbidden City. You should have time to viist other sites near to the north exit in the afternoon such as a hutong, the Yonghe Gong Lama Monastery or one of the parks. almost 7 years ago
Stay in DongCheng District, explore the Forbidden City, zhongshan park, take a subway to the Temple of Heaven and at night try some silk wormn, fried scorpions and street food at the Wangfujing night market.
Then the next day, leave early to go to Great Wall ( either Badaling or Mutianyu )
or, Summer Palace - enjoy walking in the frozen kunming lake.
almost 6 years ago