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.
Here are some photos I took on a springtime hike to Gubeikou with my wife Katie and our friends John and Courtney:
We stayed in a village at the base of the wall.
The train came very close to the wall.
A lot of this section of the wall is nothing but a trail, nowadays.
A “Great” day for hiking.
A long section of steps leading up to a tower.
There are mountains in the distance.
Which way to the Great Wall?
This abandoned house was right next to the wall. Check out those old newspapers on the walls.
Many of the hills in the area were terraced.
Now entering the Jingshanling section.
The wall snakes into the distance.
The view from a guard tower.
John and Courtney.
If you want more info about Gubeikou, or anywhere else in China, feel free to contact me.