Specifics-wise, I heard a very bad first hand (mother's) story recently about what was reportedly "the best", Yunnan University Hospital. (Disclaimer: I am not sure exactly which hospital this is, for I haven't been there) For instance, they had no idea at all about pain management options, basic nutrition, etc.
We flew to Thailand instead (last year) where there are many options. Not counting hotel and travel/visa expenses, we paid 100,000THB (18,000CNY) for a modern/clean/international hospital to do a Cesarean birth (including pre-birth tests and consultations, 3-4 days in a private hospital room, good food, etc.) While this may sound expensive it's really not compared to private hospitals in China and is light years ahead of them. Unfortunately, you can only fly a few months before the birth and thus need to take 3+ months off work (not possible for everyone).
By multiple reports (and my personal hospital experiences here for non-birth cases over 15 years) the amount of bullshit you have to go through in Chinese hospitals is ridiculous. Let's face it: giving birth is stressful enough. Unless your Chinese part of the family insists on doing it locally and you have the patience to go through with that I would strongly recommend considering Thailand.
We have used and are very happy with 昆明市妇幼保健院 for post-birth immunizations. They specialize in kids and are located just up the hill from Green Lake. (Note that every country has its own idea of which immunizations are required, and they differ by phase of moon throughout Yunnan. Note also that international serum costs a lot more here than local stuff, if you choose to use it you will be paying US$100 or so per shot instead of ~zero)
We also went to Maria pre-birth but don't rate it on professionalism or quality of experience.
You got it right, Richland is shit. A friend of mine went there for a bout of salmonella, which is pretty standard here. Instead of the normal hospital thing in China of a few stabbed needles, drips and a night in hospital (40-100RMB: I know, I've done it twice here and once in Qingdao, plus once here for another friend) they made him stay for days in an exorbitant room and used scare tactics to claim he had to pay some stupid amount of money in case of some completely unrelated situation, extra tests, etc. I felt really bad that I let him go there. He wound up paying through the nose, I believe something close to 10,000CNY.
Facts are, a lot of Chinese private hospitals are run as virtual scams and they really are dishonest.
We also went to hospitals in Australia and France (Necker, which was the first pediatric hospital in the world!), but still heartily recommend Thailand.
If you would like help with the processes in Thailand let me know, my wife and I would be happy to talk to you.