A couple weeks back I sprained my ankle in Kunming pretty badly and used GoKunming a lot for advice on hospitals, etc. I wanted to share my experience in case it's helpful to other travelers down the road.
I ended up going to Yunnan First People's Hospital because I was nervous about expensive prices as Richland International Hospital (even though that's where I was advised to go from my insurance company back home). Also I couldn't walk and Yunnan First People's was nearby. I had a hard time figuring out which public hospital was the best in Kunming, but some people had recommended it, so I gave it a shot.
All-in-all, I had a positive experience. I had to queue when I arrived and pay a 6 yuan fee to see a doctor. No one spoke much English, but people kindly pointed me in the right direction. I also came with a written description of exactly what happened to my foot in Chinese and this helped a lot. I was directed to a room with 2 young doctors and 2 assistants (presumably). They looked tired and there was a constant flow of patients coming in and out of the room, but they saw to me quickly and seemed to handle my foot - stretching it in various positions - with skill and professionalism. They wanted me to get an x-ray and made a lot of effort to translate using Baidu on their phones.
After that I had to pay for my x-ray where I originally checked in. It cost 83.8 yuan (not bad). Then I walked to an adjacent building and handed my receipt to a woman at a counter. She gave me a number for a room and I stood in line until it was my turn. 30 minutes later I had copies of my x-rays in-hand. One of the technicians spoke decent English and was very friendly. He made an effort to explain the x-ray and assured me nothing was broken (sigh of relief).
I went back to the original room of doctors with my x-rays and they tried to type a few more recommendations in the translating app (things like "cold compress").
The whole experience lasted about 1.5 hours and cost under 10 USD. I also have my x-rays in case future complications come up and I need to show them to my doctor back home. I did enough research on my own to know how to take care of my ankle if it was just a sprain, and I went to the hospital intending to get an x-ray just to make sure it wasn't broken. So the trip was successful in that regard. If I had needed detailed advice in English on how to take care of my foot (or other ailment), this would've been difficult. I definitely would not recommend the hospital if you have any serious problems that might need surgery.
Also, try to bring a friend as there was a lot of running around. Everything was in Chinese, but with some determination and patience, it was easy enough to figure out. Along each step in the process, I usually showed someone my translation of what happened to my foot and this helped a lot with the language barrier.
Hope this is helpful to someone in the future!