So, which would HN recommend? Finding a telecommute position to support life abroad or taking a job abroad?
Unless you magically have the right nationality, if you want to stay in a foreign place for any length of time you typically will need a visa, so you will need a local employer to sponsor a work permit. So if you really want to live somewhere else, take a job.
As to finding a telecommute job, it can be hard. If you want to go down that plan (i.e. telecommute in your native country and travel around abroad) I suggest you find that job and work a while in it before you start traveling.
Personally while I like traveling very much, there's nothing like really living in a different country to grow your horizons. I have lived in 4 countries - 5 if you count Scotland :-) - and don't regret any of it. If you have the interest and the opportunity, take it.
You should probably take whatever job is more interesting to you. Or perhaps you are unable to find a telecommuting job. I'm a freelancer, so I can do pretty much whatever I like. ;)