Most tourist sites have western type facilities. But still areas where you have to go to public restroom that is pretty basic.
An option is to walk into an hotel and use the bathroom there. I often do it, and have never been send away.
My wife has a clean bathroom rule not matter what country. China is not at the top, but neither is it at the bottom of our have seens or want to see, especially in major cities....and we use the hotel drop by tactic, too. We men also appreciate clean bathrooms.
Shopping malls is another option.
You mean sitting restroom. Nothing western about it as you find those squat toilets all over the world. I find sit-down toilets in most restaurants (nicer restaurants and fast food chain), hotel lobbies and shopping malls. Newer tourist attractions have them as well.
Still hard to find except in hotel and western restaurants. Many tourist places also have them. Try to time your need.
Always a good idea to take along a supply of tissues in the purse/daypack, and hand wipes/hand sanitizer.
Yeah, even if toilet is "western style" it is very rare to get soap/ tissues there. Exept hotels obv, and newer shopping malls. ALWAYS carry tissues!