This itineary is also on my mind.
However, after seeing the map of Osaka and Tokyo, cannot seem to find a way to get around.
I have problems finding the correct way to get around.
Hi, to help u out a bit, read these info-packed suggestions.
For mode of transport, have u considered:
1) Night buses like those going from SG to Genting -> this can save you nights of accommodation and also reduce $$$ damage if u only want to travel from Tokyo to Osaka or vice versa.
2) JR pass for whole of Japan. And, how many days? 7 or (14 or 21) days? -> purpose of getting JR pass is so that u can travel to many places on railways run by JR company. Bear in mind it need not be Shinkansen so u can still make day trips with JR trains.
3) Or even domestic flight?
Bonus:
4) Get those subway passes when you move around in a city [24hrs/48hrs/72hrs Tokyo Metro pass or Osaka Amazing 2/3days pass].
Before u trouble about transport, u should have the places in mind for your itinerary.
Places closer to Tokyo: Yokohama -> have cup noodles museum also, Hakone -> famous for onsen and a view of Mt Fuji; can also get to Gotemba premier outlet for discounted + tax free branded goods, Shizouka -> Mt Fuji is there, Shirakawa -> UNESCO site, Nagoya. Then there are places closer to Osaka: Kyoto -> shrines temples green tea geisha, Kobe -> beef, Nara -> aggressive and hungry deer (they chase and bite), Himeji -> famous white castle, Wakayama -> Mt Koya
With so many places, I believe u can customerise an itinerary to your liking. And then even for Osaka or Tokyo themselves, u can easily spend 2, 3 or even 4 days in one of them.
U can consider these:
1) Tokyo for a few days, Osaka for a few days. Use night buses to travel in between them. <- for your plan A
2) Flight in and out from either Tokyo or Osaka. Use maybe 7 days JR pass, visit a few cities within 6 days, get back to Tokyo/Osaka on the 7th day before JR pass expires to solve your dilemma. Cause I doubt can easily book open jaw flights at a good price. Usually flights in and out from Tokyo is cheaper than Osaka.
For example,
Why not fly in from Tokyo, use JR pass start moving west -> to Yokohama for cup noodles museum, then next stop Hakone area (stay in a Japanese ryokan with Onsen and dinner included), then move to Kansai area [Kyoto, Osaka, Kobe, Himeji area]. For Kansai area, u can either book accommodations in individual cities or use Osaka as a base, make a few day trips so don't have to drag luggage everywhere. Then on the 7th day take you final Shinkansen from Osaka back to Tokyo. Continue Tokyo itinerary from there. Or u can leave some JR pass days for Tokyo also. There are JR lines within Tokyo particularly Yamanote Line which is like our circle line -> convenient for u to travel between Ueno area, Ikebukuro and Shibuya/Shinjuku area at a shorter time. Then finally, fly off from Tokyo. Also if u can, find flights in and out of Haneda (closer to city but harder to get).