For a chance to clamber over the Great Wall, without having to deal with throngs of tourists, this Ming-dynasty section, which runs along the North Korean border, might be your best bet. 

Yibukua "one step across" near the entrance, marks a narrow point in the river between North Korea and China. Though it almost seem as if you could just hop the fence and be in the DPRK, we strongly advise you don't. There are armed soldiers hiding out, and if they catch you, they probably won't be awarding you ribbons for your fence-hopping technique. You get the drift. 

A hike down the restored portion of the wall takes you to a small, but quality museum (RMB 10 admission). Once finished, there are three options to return to the entrance. Hike bike the way you came, take the riverfront path back, or catch a ride bike with the boatmen who hang out there during the summer (RMB 20, 10 minutes). 

Some parts of the wall can be quite steep, make sure you're wearing good shoes.