The Great Wall of China (Chángchéng) about a 1 hour train trip or 1.5 hour bus ride from the city.
The Badaling section is the most famous, but also over-restored and crowded. Jinshanling, Huanghuacheng and Simatai are more distant but offer a better view of the wall away from the crowds.
Mutianyu has been restored, but is far less crowded than Badaling.
Crowds are a definite issue with the Great Wall: at popular sections at popular times, it becomes not the Great Wall of China, but rather the Great Wall of Tourists.
It is possible to rent a taxi for ¥400-800 for the round trip including waiting time.
You may want to bring a jacket against the wind or cold in the chillier season - in the summer you will need lots of water, and it will be cheaper if you bring your own.
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