There are a couple of sections where you can walk on the Great Wall: Badaling is the main one where everyone goes, Mutianyu is a little less crowded where you can ride a toboggan down the Wall, and Jinshanling/Simatai are farther out but less crowded.
We decided to go to Jinshanling with a tour organized by our hostel, since this was most recommended to us as off the beaten track, and you can hike the wall for about 6km. The tour was our most expensive attraction at 280 RMB each. It was a 2.5 hr drive out there on a Saturday, I think it can take up to 3 hrs on a weekday. When we got there, it was pretty much all Western tourists and only one other large group there. It was so nice to have the Wall pretty much to yourselves, makes for some great non-tourist-crowded photos.
We were blessed with beautiful weather as well and the sky was a vibrant blue. The moon was also already out, so the contrast was pretty striking against the bricks.
We hiked through 22 watchtowers over 2.5 hrs; the first 9 were restored in the 1980s, but past watchtower 9, it was all original Wall and much of it was crumbling.
We brought lunch and ate our sandwiches looking over the rolling mountains. Such a fabulous day and a great way to end our last full day in China! We highly recommended seeing this section of the Wall over the more touristy sections.