I noticed that no one had replied to your question. I grew up near St. Louis, Mo. and it will always remain dear to my heart.
The AF sent Jeff to University of Mo. at Columbia for his EE degree. I think that Centralia is in that general area. We were very young and had no health problems then, so I have no direct experience with docs in the area. The university has an outstanding med school, so I would think that you should be able to find some good ones in Columbia, Mo. Of course, St. Louis has both Washington Univ. and St. Louis Univ. (my alma mater), which both have major trauma centers and research hospitals.
I LOVE that area. I much prefer having four seasons, which are lovely there. The fall weather is outstanding, and I miss it terribly. If you like outdoors activities, Lake of The Ozarks can't be beat. Unfortunately, Branson has become commercialized. It wasn't that way when I was a kid. If you like sports, The St. Louis Cardinals are the greatest. I grew up making trips to the stadium to root for the Cards. There is so much to see and do in St. Louis, it would take you a long, long time to do it all.
OK, I guess that you can tell that I'm a St. Louis girl, and this is making me homesick.
I hope that the job search works out for you - let me know if you move to my beloved Missouri.