The Great Wall at Jīnshānlǐng (Jīnshānlǐng Chángchéng; admission Y40), near the town of Gǔběikǒu, has 24 watchtowers and remains relatively undeveloped. More significantly, it marks the starting point of a 10km hike to Sīmǎtái. The journey takes around four hours as the trail is steep and stony and parts of the wall have collapsed and are in a state of ruin, but it can be traversed without too much difficulty. Arriving at Sīmǎtái, however, you may have to buy another ticket.
You can do the walk in the opposite direction, but getting a ride back to Běijīng from Sīmǎtái is easier than from Jīnshānlǐng. Of course, getting a ride should be no problem if you’ve made arrangements with Simon to pick you up.