Granada, Nicaragua has private doctors that are fine. As evidence of that are the wealthy people who stay in Granada to visit the general practitioners. There are good obstetricians in Granada as well.
Granada has a good public hospital as well, which is a good place also to go for emergencies.
If you live in Granada, Hospital Metropolitano Vivian Pellas is the closest private hospital, located in Managua, about half an hour to 45 minutes away by car, on the same road that goes from Granada to Managua. This is the largest hospital in the country.
The doctors in Granada are good for general medicine, but for specialist care, you could go to Managua, which is not that far away.