The problem is your visa. If I understand correctly, you intend to move somewhere else for the experience while maintaining your current work from home job? Many countries have rules against this. You would be traveling on a tourist visa, not a work visa. While you could get away with doing your own work thing just fine, a tourist visa usually precludes you from getting other necessary services, depending on location. ie: driving license, opening bank accounts, etc. Also consider your medical coverage. I am willing to bet your current employer provided health insurance (assuming you have it) does not cover you outside of the US. Conversely, even in "free healthcare" countries like England, you can not just drop into the NHS on a tourist visa and get any service.
It is possible, but for your situation would require quite a bit of planning.
If you were actually working for a US company based outside the US or even directly for a foreign company, it would be a lot easier.
Again, YMMV depending on where you want to go.