Puerto Rico and Maryland are exempt from readmission penalties, and are still covered by Medicare. Links for Puerto Rico are below.

Foreign hospitals and doctors have their own payment systems for their residents, but still have prices for US travelers. They are not covered by Medicare, so hospital stays abroad do not incur readmission penalties, and do not count as costs in Accountable Care Organizations. Some US and international private insurance pays for foreign care. In any case costs are often much less than in the US, and specialized hospitals can give better care. Some of the best offer luxury as well as ordinary care.

Kiplinger (2017) says the book Patients beyond Borders, and its website have reviews of hospitals. I have not seen the book, but the website shows the size of each hospital, and often the total patients treated, though not the number of times doctors do any particular procedure, nor other measures of quality. You may have to ask.

NA=US Average not available to calculate percent. See link for costs abroad

Doctors identified 25 procedures and tests which may be wasteful, since they usually have low value for patients. They were given to 25% to 42% of Medicare beneficiaries each year, depending on definitions, but they only cost 0.6% to 2.7% of total Medicare costs.

In the United States, 

• 13% of medical spending goes on people who die within a year Mt.Sinai
• 25% of Medicare spending goes on people who die within a year NBER

This is because most Medicare spending goes on sick people (!), especially very sick people (!!), and some die unexpectedly (!). However very little spending goes on those who are likely to die soon.

• 5% of Medicare spending goes on people likely to die within a year (50% or more chance) NBER
• About half the people with high costs got better after an expensive treatment: heart attack, cancer treatment, etc. Mt.Sinai
• About 40% of the people with high costs have chronic conditions, and death is unpredictable Mt.Sinai
• "[R]eliably predict who will die and therefore would not benefit from receiving intensive care... turns out to be extremely hard to do. In a recent article in Science, researchers used a sophisticated machine-learning prediction tool to identify patients who are most likely to die, and found that there is no group of people for whom death is easily predictable."
  

Vox quotes economists that the US health care prices per item are abnormally high. So other countries get more health care for less cost:
"When you’re paying the highest prices in the world for basic services, for scans and drugs, it will undoubtedly be a struggle to provide all citizens with health care...

• Americans go to the doctor four times each year.
• Dutch people go to the doctor, on average, eight times each year.
• Germans make 9.9 annual doctor trips.
• Japanese residents clock in an impressive 12.8 doctor visits each year — more than three times the frequency of their American counterparts...

When Americans do go to the doctor, we tend to have less face time or interaction with our providers.

• The average hospital stay, for example, is 5.4 days in the United States.
• This puts us roughly in line with New Zealand and Norway (5.2- and 5.8-day averages, respectively) and with much shorter stays than Canadians (7.5 days) or Germans (7.8 days).

The real culprit in the United States is not that we go to the doctor too much. The culprit is that whenever we do go to the doctor, we pay an extraordinary amount."

A 2018 JAMA article compares insurance systems, and a 2008 JAMA article shows the same cost issues in 2004-6, with US doctors' salaries double the level in other countries.

​DailyKos has more detail on the range of costs.

• "America’s economic competitors discovered years ago and still share today... Whether negotiated directly or through a national association of insurers, the government sets the prices for prescription drugs, tests, treatments, hospital stays, and pretty much everything else...
• Economics, after all, is the study of the allocation of scarce resources... In the face of the infinite “wants” for healthy citizens, financially secure families, well-compensated practitioners, and strong profits for private companies of all stripes, societies must choose how and why to distribute discomfort and dissatisfaction to some or all of the constituents."

​​And DailyKos quotes the Commonwealth Fund comparisons: