Off the top of my head, I know that Finland had negligible levels of immigration until a few years ago. Several Eastern European post-Communist countries are pretty decent places to live these days (I have in mind primarily the Czech Republic), but still have no mass immigration. As far as I know, the same holds for South Korea.

Regarding emigration, the prime example were the communist countries, which strictly prohibited emigration for the most part (though, rather than looking at the numbers of emigrants, we could look at the efforts and risks many people were ready to undertake to escape, which often included dodging snipers and crawling through minefields).