3. Singapore
This is an interesting system in that the government runs a health care system that provides some care to all of its citizens, yet there remains a large private sector as well. This is largely because there is a wide split between the elite and poor in Singapore in comparison to other nations, and thus some prefer to pay for the best of the best. Yet, this by no means takes anything away from the government funded hospitals, which are held in high regard and remain relatively cheap for tourists as well. There are a plethora of options in Singapore and regardless of your budget you will be able to find reliable medical care, making it easily one of the countries with the best hospitals in the world.
