Upvote:2
They never have said anything about our taking side trips that we didn't list on our visa applications (Trips we hadn't planned at the time of the application.) The application also only asks about your current trip--no matter how long your visa is good for. If you make another trip on the same visa there's nothing that even asks for your itinerary.
We currently hold 10 year visas (no, you can't get them at present, they're only offered to Americans), that's going to be several trips they have not asked about.
As mts said in his comment, Tibet requires a special permit but otherwise we are free to wander around. Note that you might have trouble trying to find a place to sleep in a small town off the beaten track--hotels that do not expect to ever have a foreign guest likely haven't set up the procedures required to check in foreigners. Also, if you get too far off the beaten track there will be basically zero English.