One advantage of Beijing is, that you can easily get out. The Megcity has mountains in the North and West, which mark a sharp boundary between 1950s style coal power plants and a beautiful natural landscape. You might want to avoid tourist destinations, but still use public transport. And actually, this is quite well possible.
For example take the subway to Ping Guo Yuan (=Apple Garden, but don't be confused when you don't see any apple tree). It is the last stop of Line 1 in the West. Then walk 300 meters further West, until you see the bus stop for line 892. The bus service starts at 7:00 o'clock in the morning and runs very frequently. Stay on the bus for about 2 hours and get off at at the Fa Cheng bus stop, at N40 00.113 E115 47.949. This is a good starting point for a hike over the mountains and the decent to Jian Yuntai (N39 56.132 E115 51.110), for the bus 929 back to Ping Guo Yan station. The whole hike will take you around 7 hours. The last bus at Jian Juntai leaves at 17:40. If you miss that, you are (!) in trouble, as this is just a remote village which has no (!) other transportation.
The route gives a beautiful outlook over the mountains. There are nearly no people up there. The villagers do not grow nuts or fruits like in other rural regions around Beijing. Still the terraces along the slopes witness an agricultural past here. The trails are just kept open by a few hikers per year and you need a thorn proof jacket. Strictly stay on the trails, which are occasionally steep and going along fringes. Hikers here use 435.000 MHz and 437.900 MHz.