We've been fortunate enough to do a couple of round the world trips.
Would definitely recommend Japan, but you would need more than 3/4 days there, and Oz and NZ have to be on the list too.
Going east and returning via the States is a weird sensation. We left Auckland at 3pm one day, arrived at LA 6am the same day, 9 hours before we left, and that after a 12 hour flight!
As suggested, Trailfinders is a good place to start, we bought a round the world ticket, flying with Qantas and BA, and it allowed us several, sorry can't remember exactly how many, stop overs.
Enjoy!