Choayang Park is like Central Park in Beijing, not sure I'd call that off-grid.
If you want something a bit different and see people's daily life then get lot in hutongs. You could go to Liulichang and make you way towards Qianmen walking through the hutongs. Except for the starting and end points, you probably won't see many tourists if any.
There are also a number of "wet markets" all over town but they are buried in residential districts and hard to find.
One seldom visited tourist attractiuon is the Marco Polo bridge (Lugouqiao: http://www.lugouqiao.org.cn/). You have also the nearby Japanese War Memorial. Short of going to Nanjing, this will help you understand why Chinese dislike Japanese so much.
Obviously, another way to rub shoulders with locals is to go to any major park in early morning or after dinner. Early morning at the Temple of Heaven is great for people watching.