I plan to do some hiking near and on portions of the Great Wall. My question is about the places that are not the top tourist spots, like Jinshanling, Zhuangdaokou or Shui Changcheng. Are such places easily accessible by any kind of public or cheap transportation?
I visited the wall many times during my time in China, and my favorite place by far was Mutianyu (慕田峪). It is breathtakingly beautiful, and was not crowded at all when I went. It's not the best place if you're looking for truly remote, but it's not nearly as crowded as the more popular sections of the wall like badaling. I suggest you walk a bit further down (an idea is to go up near the toboggan and walk to your right up the hills to the multiple guard posts), because on the three occasions I went there almost no one walked there. I think the main reason is that people go to the main entry point and are too tired to walk past the toboggan. However, the history there is incredible and it is just like the pictures.
If you're looking for truly remote there are overnight camping trips which range from a night or two to a couple of weeks (I met a couple from America who were on a 3 week camping tour!). I was also talking to some of my Chinese friends and, apparently, if you're willing to travel very far, there are extremely remote and almost untouched areas of the wall much further north (like near Mongolia), but that would really require a Mandarin-speaking tour guide.
In terms of transport to places like Mutianyu, it can be difficult if you don't speak Mandarin. The first two times I went, I went in a hotel shuttle, and the other time I went in a friend's car. However, I stayed at two hostels for a few nights and they both had trips that could accommodate Westerners and locals to Mutianyu/other less popular places that ran during the week. However, I found these were at slightly inconvenient times but that may not be the case for everywhere.. I don't think it should be a problem though.
You could try the Dongzhimen Bus Terminal; there are buses to a few Great Wall areas over there. However, you must be able to communicate in Mandarin to maneuver around effectively.
Otherwise, you might want to find fellow hikers so that you could go with them.