Did they know about Europe or Africa? I know Roman glass beads have been found in an Ancient Japanese tomb, so I'm wondering if maybe they atleast knew about some of the empires in the west, or the cartography.
The Han Chinese knew a decent amount, but largely shrouded in myth. Here is a list of historical documents:
http://depts.washington.edu/silkroad/texts/texts.html
The ones translated by John Hill are the best. There are descriptions and names for the chief cities of the Eastern empire, primary exports, notable flora, some not entirely nonsensical reports about the Roman political system, and so on.
The Japanese, at least as late as the Heian period, knew very little about the world beyond China, Korea, and Central Asia. One writer has his character shipwrecked in Persia while sailing from Japan to China, which should give you an idea.
Which Asian people? [Asia is a very large continent](https://en.wikipedia.org/wiki/File:Asia_(orthographic_projection).svg). The known world for someone from Jerusalem is going to be much different than that of someone in Indonesia, Japan, or Siberia.
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