Agree with other posters on tastes being personal - but here are a few suggestions

LA - Getty museum, Hire car and drive out to the observatory on a day its open - mountain drive is very beautiful
Pop Hawaii into the stops as you can go oneworld to Tokyo from there. Then go diving / snorkeling with Mantas there. Catch some waves too.
Tokyo - no advice here apart from avoid the lounge food
Sydney - not done the touristy thing here just short business trips
NZ - did a 5 week hol here - North island - north of auckland - Piha (Nice beach and waves), coromandel. South island - milford sound, fox glacier (helicopter drop off if you can stretch to it - I regret not doing that), albatross sanctuary in far south but only if time allows

gene