It is not a perfect fit for what you want, but check the Wikitravel article on "retiring abroad" for info on various places that are cheap to live and that do encourage immigration: http://wikitravel.org/en/Retiring_abroad
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There are quite a few tiny computers available, Rasberry Pi and the like. Alone, they don't solve my problem because you need a screen and that is at least as heavy as a laptop. However, there are also quite a few tiny projectors (e.g. see http://www.fastcompany.com/blog/noah-robischon/editors-desk/10-tiny-mighty-pico-projectors-photo-gallery). Would a tiny computer plus a tiny projector do the trick? Which ones? All I need for software is some open source Unix (any *BSD or LInux distro should be fine, or even Minix), a browser and an editor. I don't need large storage or a fast CPU.
Has anyone done something like this? Does anyone have a recommendation for either the computer or the projector?"