There are countries in Europe that let you retire there if you have the money. Pick out the one you want and then check their visa options. But, before making any life changing decisions, visit the area first.
American citizens can stay in most European countries for up to 6 months without a visa. Go, see if you like it. Maybe check out a few countries.
I don't know the details of your illness, but bring a list of your medication so you can have it refilled if needed. You can also register as a temporary patient at a local doctor. They can then refer you to any specialists you may need.
Get some travelling insurance for any unexpected medical expenses that might occur. Check the rules the country has regarding non-citizens accessing their health services. Some countries just have an upfront fee.
You don't need to go through all the effort with shifting cash to x to cash. The US is one of the only countries that taxes its citizens abroad. And the US has agreements with many European countries, so the IRS doesn't care which bank or where.
The massive 'exit tax' is for those renouncing their citizenship, which you cannot do, unless you have a second citizenship to replace it.
Exchange rates for transferring the dollar to whatever the new currency is, is what'll cost you, because there is a fee from the banks or whichever exchange you have do it. But you'd potentially lose that shifting from cash to x to cash.
If you're not in good health, just keep it simple and focus on recovery.
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