in the 1950s. See: Why is there so much migration between Japan and Brazil? )
There really only has been one big wave of emigration from Japan in modern history. This occured in the early 20th century when a large number of people went (lured by various promises, many of which turned out to be false) to the U.S., Hawaii (before it was a state), Brazil, and to a lesser extent to western Canada.
After the war, Japanese emigration to the west may have been curtailed because 1. Japan lost a huge number of young men to the war, and needed a lot of able bodies, 2. the Economic Miracle of the 1950s-80s, and 3. possibly fear of discrimination and recism (remember that many Japanese-Americans were interned by the U.S. and Canadian governments during the war).
There were a large number of temporary Japanese residents in the U.S. in the 70s to the 90s, mainly businessmen on temporary assignment and students. Most of these people never intended to stay overseas permanently, and have since returned. There are fewer of these temporary expats these days, for a number of reasons: 1. Japanese multinational companies are hiring locally more, rather than staffing with Japanese employees sent over from the home office, and 2. because of the current economic climate, young people don't feel they have the time or resources to spend time abroad.
But probably the biggest reason you don't see a lot of Japanese students in American universities these days is that an American education is not really regarded as an advantage back home. (I believe that in South Korea and China it is regarded as a big advantage.) If anything, time away from the Japanese system can be regarded as a hindrance. This depends on the industry of course, but that's the general perception.
And as for why permanent emigration is not big in Japan...well, most Japanese people these days are rather content with their own country, regarding it as the best place to live in the world. (This way of thinking may sound familiar to Americans, maybe? ^_^) The main impetus for emigrating it get get a 'better life' elsewhere...and if you think you have it best anyway, why bother? Some pundits see this is a negative, a return to isolationist ways and false nationalism. But there you are. (And even in terms of imported culture, stuff from France and Europe, as well as other Asian cultures, are arguably more 'in' in Japan at the moment than American stuff, with the exception of Hawaii.)