Our kids were not born in Kansas City, so I can't give specific info about the maternity services, but I will tell you what to look for, and that is a Level III Neonatal Intensive Care Unit (NICU). All hospitals claim to have a NICU, but make sure it is Level III, which is the designation for the ability to handle the most critical cases.
Attractive rooms, areas for families to be together, and all that other stuff is nice. I don't want to knock any of that. But the bottom line is that none of it matters in comparison to being able to bring home a healthy kid. Our first child was born 6 weeks early, and thank heaven the hospital was equipped to care for him. If we had been at another hospital, they might have had to put him in an ambulance or a helicopter. <shudder> As it was, he was right where he needed to be, and everything turned out okay. But I would never have been able to forgive myself if we had picked out a hospital just because it had beautiful rooms. In the KC area, I believe that Research Medical Center, Centerpoint, Truman, the University of Kansas Medical Center and Overland Park Medical Center have a Level III unit. There might be others, but you would need to ask.
You can get more info about labor and delivery hospitals in the area at the Web page below:
I wish you the best and I wish you some sleep. Haha . Good luck on that one. ;-)