I've got a driver who I call up for pickup and dropoff between Huairou urban area and various Great Wall or other hiking locations in Huairou like Jiankou, Mutianyu, Huanghuacheng, Moyashike, etc. She's a really nice woman with a mianbao che that can accommodate 4-5 people with big backpacks. She also has a son who's trying to get into a decent university but needs English tutoring (his other subjects are fine). He already took the gaokao once and didn't get a good enough score, so he's going to try again this year.
She asked me to help her kid practice English periodically, but I don't have the kind of flexibility to make that time commitment. However, if anyone here does have that flexibility (you can discuss with her using Wechat/Weixin or other remote methods as well as occasional in-person visits), she would be able to give a serious discount -- probably free rides to/from hiking destinations in Huairou, and would probably treat you to meals as well. I figure it's a win-win for anyone who has the time.
She doesn't speak English, but I can help make an introduction if you like. Her surname is 纪 (Ji4) -- I call her 纪姐. Her cell is 135 five two 00 three nine 2 five.
If you'd like me to help make an introduction, just let me know!