Originally Posted by MSPeconomist

The above advice is excellent. I would add that you might want to visit the Imperial Palace in Tokyo. In Osaka, IMO the main tourist place of historical interest would be the castle. Otherwise, Osaka is just a big modern business city that seems much less international than Tokyo.

Note that the Tokyo and Kyoto/Osaka areas have somewhat different cultures and cuisines, including the preparation of tempura. If you're interested in these aspects, plan to have a multicourse traditional seasonal meal in Kyoto. Also in Kyoto, don't miss the area with the geisha, ideally strolling the side streets in late afternoon to early evening.

Do you want to try to spend a night in a ryokan?