Go to where? This is a good question, especially if you are from USA.
About Asia:
The major question is how much money do you have? Can you find a job with good income in the country of destination?
What about visa/working permit? Personal safety? Medical care and insurance? Can you buy your accommodation there and so on....
If you really have a lot of money you can go almost everywhere worldwide, the US-passport is not that bad for international travel and long-stay but only if you do not bother the locals teaching them how much better all and everything is in the States.
However here in Japan, the US-dollar lost over the last decades more than 70 percent of its value... People who get their salary in USD, like US-military servicemen are now financially pretty down.
Many countries in Asia have also their problems and are anything but stable and often not so welcoming to foreigners
South Korea is facing North Korea and is not a cheap place and rather crowded
Taiwan is always aware it might be attacked by China anytime, HongKong is gone already...
China is not my favorite anyway, and if you are US-citizen be careful and aware of political problems between China and USA.
Philippines is a poverty place and has serious problems with criminality
Singapore is nothing but a city-state and fairly expensive.
Thailand is not bad for short-time, but long-stay requires a lot of paperwork, not really so welcoming and recently not so cheap anymore.
Countries which were promising in the past, like Lebanon and even Iran - forget about them.
There are various countries which are nothing but headache - Pakistan and Bangladesh, North Korea and Afghanistan etc.
Others might welcome you, but there is not much there... like Mongolia or some former Soviet-Union countries
If you have money and are retired, Malaysia is not so bad, but to buy property there as a foreigner does not make sense, too many restrictions.
I heard many positive comments about Nepal, but I have no experience about it... anybody knows more about this country?
Some people mention Indonesia, but I am not sure about long-stay permits...
Concusion: if you are in Asia, keep always an escape route in your mind, never bring all money into Asia - so you can move on anytime in case of trouble.