There are so many places on this planet worth visiting. It all depends where you already have been, if you like cities, beach, mountains, food, culture.
In any case don't squeeze too much into not enough days. 3 or 4 days for a big city, another 5 to 8 if you want to see the countryside per stop.

It is like: "I am hungry. What should I eat."

My personal preference would be:
Spend less time in LA.
Fiji is somewhat overrated, but good for a few days if it is easy to get there. There are better islands, also many beaches in Asia are nicer
NZ is very beautiful, but a bit boring after a while
Sydney is a great place (consider hopping over to Uluru)
Tokyo is interesting (Side trip to Kyoto?)
I would add Hong Kong and/or Bangkok and/or Saigon.

Why not concentrate on places where it is difficult to get to (Fiji, Australia, NZ). It will be easy to jump over to NY or LA for a few days in the future.Same is true for many places in Asia.