We did a 5-month trip hitting some of those spots. We spent 3 weeks in the South Island of NZ but 2 weeks would be plenty, we spent 3 days in Sydney (plenty), 3 days in the Hunter Valley (more than enough), 3 days in the Blue Mtns (we love hiking) and 5 days in Melbourne (more than enough), 2 weeks in Fiji (plenty) and 3 days in NYC (plenty--I used to live there). I would say you want to plan at least 1 week in Tokyo and you should go to Kyoto/Nara. As for LA (where I live now) 3 or 4 days is enough if you just want to stay around the city--you will need a car to get around.
I can't comment on airfare because we bought single tickets.