Hiking on the Gubeikou Great Wall
Having lived in Beijing for the last three years, Katie and I have visited the Great Wall many times. Contrary to popular belief, the Great Wall isn't one continuous wall. There are many sections; some have eroded to almost nothing, others remain relatively intact, and still others that have been completely restored to their former glory. My favorite sections (as you probably guessed) are un-restored, yet still hike-able.
Gubeikou (古北口) fits the bill perfectly. It's one of the easier sections to hike, it typically draws few tourists, and the surrounding landscape is spectacular. It's only a few short hours from Beijing, so if the Great Wall is on your travel radar, Gubeikou is a great section to consider visiting.