Jetstar asia is servicing Japan only towards Australia, so it is difficult to get there really cheap.
A return ticket will cost you around 600-700€ depending on travel date. Search for deals here
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From Shanghai or Bejing you can fly to Tokyo for aprox 160€ (one way) but the flights to either city are around 400€ so you´d be better of buying a return trip.
As far as i know there are ferries servicing Shanghai -> Japan but they are not really cheaper than flying, and you would need a visa for china.
Avoid traveling during Golden week and Obon.
Summer is hot in the south (and alot of rain) but can be really nice up north (hokkaido). Winter can be cold in the northern parts, ok in the south. Spring is nice because of the cherry blossoms and autum is great to see the autum foilage. So it depends on what you want to see.